You searched for subject:(High Order Methods).
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University of California – Berkeley
1.
Fortunato, Meire.
Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations.
Degree: Mathematics, 2016, University of California – Berkeley
URL: http://www.escholarship.org/uc/item/0zc4s5sv 
► High-order methods are receiving considerable interest from the computational community because they can achieve higher accuracy with reduced computational cost compared to traditional low-order approaches.…
(more)
▼ High-order methods are receiving considerable interest from the computational community because they can achieve higher accuracy with reduced computational cost compared to traditional low-order approaches. These methods generally require unstructured meshes of non-inverted curved elements, and the generation of high-order curved meshes in a robust and automatic way is an important and challenging open problem.We present a method to generate high-order unstructured curved meshes by solving the classical Winslow equations using a new continuous Galerkin finite element discretization. This formulation appears to produce high quality curved elements, which are highly resistant to inversion. In addition, the corresponding nonlinear equations can be solved efficiently using Picard iterations, even for highly stretched boundary layer meshes. Another challenge that mesh-based methods face is that the discretization of the domain is usually generated before the solution is known, which can lead to large numerical errors or non-convergent schemes. A tool that can be used to overcome this problem is mesh adaptivity. We use the Winslow variable diffusion equations – which are a variation of the classical form – to perform curved and anisotropic unstructured mesh adaptivity. We use a range of numerical examples to validate our models including complex geometries and stretched boundary layers. We demonstrate the high quality of the generated meshes and the performance ofthe nonlinear solver. Finally, we present an example of mesh adaptivity for shock capturing when solving the Euler equations of gas dynamics for supersonic flow.
Subjects/Keywords: Mathematics; High-order curved mesh adaptivity; High-order curved mesh generation; High-order methods
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APA (6th Edition):
Fortunato, M. (2016). Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations. (Thesis). University of California – Berkeley. Retrieved from http://www.escholarship.org/uc/item/0zc4s5sv
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Fortunato, Meire. “Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations.” 2016. Thesis, University of California – Berkeley. Accessed April 16, 2021.
http://www.escholarship.org/uc/item/0zc4s5sv.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Fortunato, Meire. “Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations.” 2016. Web. 16 Apr 2021.
Vancouver:
Fortunato M. Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations. [Internet] [Thesis]. University of California – Berkeley; 2016. [cited 2021 Apr 16].
Available from: http://www.escholarship.org/uc/item/0zc4s5sv.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Fortunato M. Curved and anisotropic unstructured mesh generation and adaptivity using the Winslow equations. [Thesis]. University of California – Berkeley; 2016. Available from: http://www.escholarship.org/uc/item/0zc4s5sv
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Mississippi State University
2.
Yassir, Sofia.
Effect of small steps on the receptivity and transition in high speed boundary layer.
Degree: MS, Aerospace Engineering, 2016, Mississippi State University
URL: http://sun.library.msstate.edu/ETD-db/theses/available/etd-10262016-131543/
;
► The research on transition in supersonic and hypersonic boundary layers has been reinvigorated in the last decades because of the increased interest in high-speed…
(more)
▼ The research on transition in supersonic and hypersonic boundary layers has been reinvigorated
in the last decades because of the increased interest in
high-speed flight. The
receptivity to environmental disturbances of
high-speed boundary layers developing over
flat plates or curved surfaces is a very important problem because the transition process
is directly impacted by it. The main objective of the research is to determine the effect
of small steps on laminar
high-speed boundary-layers that are excited by freestream disturbances
in the form of vorticity and acoustic waves. Both supesonic and hypersonic
regimes are analyzed using a
high-
order compressible Navier-Stokes numerical algorithm.
It is found that both the backward and the forward steps are capable of stabilizing the disturbances
that propagate inside the boundary layer. This will potentially delay the formation
of three-dimensional disturbances that are precursors to transition into turbulence.
Advisors/Committee Members: Adrian Sescu (committee member), David S. Thompson (committee member), J. Mark Janus (committee member).
Subjects/Keywords: high-order methods; receptivity; boundary layer transition
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APA (6th Edition):
Yassir, S. (2016). Effect of small steps on the receptivity and transition in high speed boundary layer. (Masters Thesis). Mississippi State University. Retrieved from http://sun.library.msstate.edu/ETD-db/theses/available/etd-10262016-131543/ ;
Chicago Manual of Style (16th Edition):
Yassir, Sofia. “Effect of small steps on the receptivity and transition in high speed boundary layer.” 2016. Masters Thesis, Mississippi State University. Accessed April 16, 2021.
http://sun.library.msstate.edu/ETD-db/theses/available/etd-10262016-131543/ ;.
MLA Handbook (7th Edition):
Yassir, Sofia. “Effect of small steps on the receptivity and transition in high speed boundary layer.” 2016. Web. 16 Apr 2021.
Vancouver:
Yassir S. Effect of small steps on the receptivity and transition in high speed boundary layer. [Internet] [Masters thesis]. Mississippi State University; 2016. [cited 2021 Apr 16].
Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-10262016-131543/ ;.
Council of Science Editors:
Yassir S. Effect of small steps on the receptivity and transition in high speed boundary layer. [Masters Thesis]. Mississippi State University; 2016. Available from: http://sun.library.msstate.edu/ETD-db/theses/available/etd-10262016-131543/ ;
University of Toronto
3.
Shen, Xiaoyue.
Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations.
Degree: 2017, University of Toronto
URL: http://hdl.handle.net/1807/79785
► Third- and fourth-order methods have been implemented to solve the steady Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model. Summation-by-parts operators are used for spatial…
(more)
▼ Third- and fourth-order methods have been implemented to solve the steady Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model. Summation-by-parts operators are used for spatial discretization along with simultaneous approximation terms to enforce boundary and interface conditions in a weak sense. Two validation cases are tested to verify the high-order implementation of the turbulence model and to examine the efficiency and robustness of the high-order methods. It is shown that the third-order method generally produces the most accurate results on a given mesh. The use of the fourth-order method also shows the potential of increasing numerical accuracy over the second-order method on coarse meshes. In terms of computational cost, the results demonstrate that the high-order methods are more efficient as the same level of accuracy can be achieved within less computational time on a coarser mesh.
M.A.S.
Advisors/Committee Members: Zingg, David W, Aerospace Science and Engineering.
Subjects/Keywords: High-Order Methods; Turbulence Modelling; 0538
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APA ·
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APA (6th Edition):
Shen, X. (2017). Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/79785
Chicago Manual of Style (16th Edition):
Shen, Xiaoyue. “Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations.” 2017. Masters Thesis, University of Toronto. Accessed April 16, 2021.
http://hdl.handle.net/1807/79785.
MLA Handbook (7th Edition):
Shen, Xiaoyue. “Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations.” 2017. Web. 16 Apr 2021.
Vancouver:
Shen X. Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations. [Internet] [Masters thesis]. University of Toronto; 2017. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1807/79785.
Council of Science Editors:
Shen X. Application of High-order Summation-by-parts Operators to the Steady Reynolds-averaged Navier-Stokes Equations. [Masters Thesis]. University of Toronto; 2017. Available from: http://hdl.handle.net/1807/79785
Rice University
4.
Lin, Yimin.
Entropy Stable Discontinuous Galerkin-Fourier Methods.
Degree: MA, Computational & Applied Math, 2020, Rice University
URL: http://hdl.handle.net/1911/109373
► Entropy stable discontinuous Galerkin methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such methods depends on summation-by-parts (SBP)…
(more)
▼ Entropy stable discontinuous Galerkin
methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such
methods depends on summation-by-parts (SBP) operators and flux differencing using entropy conservative finite volume fluxes. In this work, we propose a discontinuous Galerkin-Fourier method for systems of nonlinear conservation laws, which is suitable for simulating flows with spanwise homogeneous geometries. The resulting method is semi-discretely entropy conservative or entropy stable. Computational efficiency is achieved by GPU acceleration using a two-kernel splitting. Numerical experiments in 3D confirm the stability and accuracy of the proposed method.
Advisors/Committee Members: Chan, Jesse (advisor).
Subjects/Keywords: Numerical PDEs; High order methods; Discontinuous Galerkin methods; High performance computing
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APA ·
Chicago ·
MLA ·
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CSE |
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Manager
APA (6th Edition):
Lin, Y. (2020). Entropy Stable Discontinuous Galerkin-Fourier Methods. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/109373
Chicago Manual of Style (16th Edition):
Lin, Yimin. “Entropy Stable Discontinuous Galerkin-Fourier Methods.” 2020. Masters Thesis, Rice University. Accessed April 16, 2021.
http://hdl.handle.net/1911/109373.
MLA Handbook (7th Edition):
Lin, Yimin. “Entropy Stable Discontinuous Galerkin-Fourier Methods.” 2020. Web. 16 Apr 2021.
Vancouver:
Lin Y. Entropy Stable Discontinuous Galerkin-Fourier Methods. [Internet] [Masters thesis]. Rice University; 2020. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1911/109373.
Council of Science Editors:
Lin Y. Entropy Stable Discontinuous Galerkin-Fourier Methods. [Masters Thesis]. Rice University; 2020. Available from: http://hdl.handle.net/1911/109373
Rice University
5.
Lin, Yimin.
Entropy Stable Discontinuous Galerkin-Fourier Methods.
Degree: MA, Engineering, 2020, Rice University
URL: http://hdl.handle.net/1911/109372
► Entropy stable discontinuous Galerkin methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such methods depends on summation-by-parts (SBP)…
(more)
▼ Entropy stable discontinuous Galerkin
methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such
methods depends on summation-by-parts (SBP) operators and flux differencing using entropy conservative finite volume fluxes. In this work, we propose a discontinuous Galerkin-Fourier method for systems of nonlinear conservation laws, which is suitable for simulating flows with spanwise homogeneous geometries. The resulting method is semi-discretely entropy conservative or entropy stable. Computational efficiency is achieved by GPU acceleration using a two-kernel splitting. Numerical experiments in 3D confirm the stability and accuracy of the proposed method.
Advisors/Committee Members: Chan, Jesse (advisor).
Subjects/Keywords: Numerical PDEs; High order methods; Discontinuous Galerkin methods; High performance computing
Record Details
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❌
APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Lin, Y. (2020). Entropy Stable Discontinuous Galerkin-Fourier Methods. (Masters Thesis). Rice University. Retrieved from http://hdl.handle.net/1911/109372
Chicago Manual of Style (16th Edition):
Lin, Yimin. “Entropy Stable Discontinuous Galerkin-Fourier Methods.” 2020. Masters Thesis, Rice University. Accessed April 16, 2021.
http://hdl.handle.net/1911/109372.
MLA Handbook (7th Edition):
Lin, Yimin. “Entropy Stable Discontinuous Galerkin-Fourier Methods.” 2020. Web. 16 Apr 2021.
Vancouver:
Lin Y. Entropy Stable Discontinuous Galerkin-Fourier Methods. [Internet] [Masters thesis]. Rice University; 2020. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1911/109372.
Council of Science Editors:
Lin Y. Entropy Stable Discontinuous Galerkin-Fourier Methods. [Masters Thesis]. Rice University; 2020. Available from: http://hdl.handle.net/1911/109372
University of Toronto
6.
Tobaldini Neto, Luiz Tobaldini.
High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames.
Degree: PhD, 2019, University of Toronto
URL: http://hdl.handle.net/1807/97004
► A novel, parallel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is developed and applied to large-eddy simulation (LES) of turbulent premixed flames. The high-order…
(more)
▼ A novel, parallel,
high-
order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is developed and applied to large-eddy simulation (LES) of turbulent premixed flames. The
high-
order CENO finite-volume scheme is applied to the solution of the Favre-filtered Navier-Stokes equations governing turbulent flows of a fully compressible reactive mixture on a three-dimensional, multi-block, body-fitted, computational mesh consisting of hexahedral volume elements. The CENO method uses a hybrid reconstruction approach based on a fixed central stencil. The discretization of the inviscid fluxes combines an unlimited
high-
order least-squares reconstruction technique based on the optimal central stencil with a monotonicity preserving, limited, linear, reconstruction algorithm. Switching in the hybrid procedure is determined by a smoothness indicator such that the unlimited
high-
order reconstruction is retained for smooth solution content that is fully resolved and reverts to the limited lower-
order scheme, enforcing solution monotonicity, for regions with abrupt variations (i.e., discontinuities and under-resolved regions). The
high-
order viscous fluxes are computed to the same
order of accuracy as the hyperbolic fluxes based on a
high-
order accurate cell interface gradient derived from the unlimited, cell-centered, reconstruction. The proposed cell-centered finite-volume scheme is formulated for three-dimensional multi-block mesh consisting of generic hexahedral cells and applied to LES of premixed flames. For the reactive flows of interest here, a flamelet-based subfilter-scale (SFS) model is used to describe the unresolved influences of interaction between the turbulence and combustion. This SFS combustion model is based on a presumed conditional moment (PCM) approach in conjunction with flame prolongation of intrinsic low-dimensional manifold (FPI) tabulated chemistry. Numerical results are discussed for a laboratory-scale lean premixed methane-air Bunsen-type flame. The performance of the proposed
high-
order scheme for turbulent reactive flows is analysed by a systematic mesh refinement study using different spatial orders of accuracy.
Advisors/Committee Members: Groth, Clinton P.T., Aerospace Science and Engineering.
Subjects/Keywords: Aerospace; Combustion; Computational Fluid Dynamics; High-Order Methods; Numerical Methods; 0538
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APA (6th Edition):
Tobaldini Neto, L. T. (2019). High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/97004
Chicago Manual of Style (16th Edition):
Tobaldini Neto, Luiz Tobaldini. “High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames.” 2019. Doctoral Dissertation, University of Toronto. Accessed April 16, 2021.
http://hdl.handle.net/1807/97004.
MLA Handbook (7th Edition):
Tobaldini Neto, Luiz Tobaldini. “High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames.” 2019. Web. 16 Apr 2021.
Vancouver:
Tobaldini Neto LT. High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames. [Internet] [Doctoral dissertation]. University of Toronto; 2019. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1807/97004.
Council of Science Editors:
Tobaldini Neto LT. High-order Finite-volume CENO Scheme for Large-Eddy Simulation of Premixed Flames. [Doctoral Dissertation]. University of Toronto; 2019. Available from: http://hdl.handle.net/1807/97004
University of Illinois – Chicago
7.
Abbassi, Hessamoddin.
Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization.
Degree: 2014, University of Illinois – Chicago
URL: http://hdl.handle.net/10027/19134
► High-fidelity simulation of supersonic flows is a powerful tool for gaining insight into the complex physics of such flows at a fraction of cost and…
(more)
▼ High-fidelity simulation of supersonic flows is a powerful tool for gaining insight into the complex physics of such flows at a fraction of cost and time of experiments. The availability of supercomputers has made massively parallel numerical simulations a viable option and has inspired a vast amount of research efforts to develop accurate and affordable numerical tools for simulation of real world engineering problems.
The accurate simulation of supersonic flows is well suited to higher-
order computational fluid dynamics (CFD). Since these cases often involve flow accompanied by strong shock waves, an appropriate shock capturing technique for higher-
order methods is necessary. Among the numerous available
methods for shock capturing, adding artificial viscosity seems to be the most promising option which has been successfully implemented in classical numerical schemes, e.g. finite volume
methods. In this research we embark upon the implementation of an artificial viscosity shock capturing technique in a
high-
order discontinuous Galerkin (DG) method to accurately simulate shock dominated flows.
The artificial viscosity model used in this work is a modified form of the entropy viscosity (EV) method. The artificially added viscosity is proportional to the local size of an entropy production. The entropy satisfies a conservation equation only in the regions where the solution is smooth and satisfies an inequality in shocks. The basic idea used in entropy viscosity method is based on the assumption of a large entropy production at shocks. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions and large in shocks, the dissipation will be virtually added only to shocked regions. However, direct implementation of the entropy viscosity method in our discontinuous spectral element method (DSEM) leads to a non-smooth artificial viscosity, which in turn leads to oscillations and instability of the solution. To smooth the artificial viscosity, the EV method is coupled with a spectral filter and an interface treatment technique. The resulting artificial viscosity is locally large near discontinuities and transitions smoothly to zero in smooth flow regions. The method enables using elements with orders higher than unity while avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme.
Since supersonic flows are, by definition,
high speed and naturally turbulent, the shock capturing method should be capable of resolving shocks in presence of turbulence. Consequently, the use of method is extended to compressible turbulence and a special emphasis is placed on distinguishing strong oscillations associated with turbulence from shock waves. A modified formulation incorporating a shock sensor is proposed for turbulent flows and the obtained results confirm the ability of the modified method to capture shocks while preserving the main features of the turbulence structure.
Advisors/Committee Members: Mashayek, Farzad (advisor), Brezinsky, Kenneth (committee member), Aggarwal, Suresh K. (committee member), Jacobs, Gustaaf (committee member).
Subjects/Keywords: Supersonic Flow; Computational Fluid Dynamics; High order Methods; Turbulence; Shock Capturing
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APA (6th Edition):
Abbassi, H. (2014). Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization. (Thesis). University of Illinois – Chicago. Retrieved from http://hdl.handle.net/10027/19134
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Abbassi, Hessamoddin. “Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization.” 2014. Thesis, University of Illinois – Chicago. Accessed April 16, 2021.
http://hdl.handle.net/10027/19134.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Abbassi, Hessamoddin. “Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization.” 2014. Web. 16 Apr 2021.
Vancouver:
Abbassi H. Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization. [Internet] [Thesis]. University of Illinois – Chicago; 2014. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/10027/19134.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Abbassi H. Supersonic Flow Simulation with Entropy-Based Artificial Viscosity Stabilization. [Thesis]. University of Illinois – Chicago; 2014. Available from: http://hdl.handle.net/10027/19134
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Ottawa
8.
Lin, Yaoyao.
Improvements in Obreshkov-based High-Order Circuit Simulation Method
.
Degree: 2015, University of Ottawa
URL: http://hdl.handle.net/10393/32090
► The transient time-domain simulation, of the circuit response, is a fundamental component in the Computer-Aided Design tools of all integrated circuit and systems. It is…
(more)
▼ The transient time-domain simulation, of the circuit response, is a fundamental component in the Computer-Aided Design tools of all integrated circuit and systems. It is typically desirable that a method adopted in the transient circuit simulator be of high- order and numerically stable. The two requirements, however, proved to be in conflict with each other, especially in the larger class of methods that were used in traditional circuit simulators. Recent work based on utilizing the Obreshkov formula has proved that it is possible to combine the high order with the numerical stability.
The objective of this thesis is to show how the present implementation of the Obreshkov- based method can be improved and generalized to handle different types of circuits. The first aspect of improvement targets the computation of the high-order derivatives re- quired by the Obreshkov formula. The second aspect of improvement, presented in the thesis, develops a generalized formulation that takes into account the presence of non- linear memory elements, whose nonlinearity is based on a capacitive or inductive-based nonlinear model.
Subjects/Keywords: A-stable;
Circuit simulation;
Nonlinear memory elements;
High-order integration methods
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APA ·
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Export
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APA (6th Edition):
Lin, Y. (2015). Improvements in Obreshkov-based High-Order Circuit Simulation Method
. (Thesis). University of Ottawa. Retrieved from http://hdl.handle.net/10393/32090
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Lin, Yaoyao. “Improvements in Obreshkov-based High-Order Circuit Simulation Method
.” 2015. Thesis, University of Ottawa. Accessed April 16, 2021.
http://hdl.handle.net/10393/32090.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Lin, Yaoyao. “Improvements in Obreshkov-based High-Order Circuit Simulation Method
.” 2015. Web. 16 Apr 2021.
Vancouver:
Lin Y. Improvements in Obreshkov-based High-Order Circuit Simulation Method
. [Internet] [Thesis]. University of Ottawa; 2015. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/10393/32090.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Lin Y. Improvements in Obreshkov-based High-Order Circuit Simulation Method
. [Thesis]. University of Ottawa; 2015. Available from: http://hdl.handle.net/10393/32090
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Cambridge
9.
Trojak, William.
Numerical Analysis of Flux Reconstruction.
Degree: PhD, 2020, University of Cambridge
URL: https://www.repository.cam.ac.uk/handle/1810/304614
► High-order methods have become of increasing interest in recent years in computational physics. This is in part due to their perceived ability to, in some…
(more)
▼ High-order methods have become of increasing interest in recent years in computational
physics. This is in part due to their perceived ability to, in some cases, reduce the computational overhead of complex problems through both an efficient use of computational
resources and a reduction in the required degrees of freedom. One such high-order
method in particular – Flux Reconstruction – is the focus of this thesis. This body of work
relies and expands on the theoretical methods that are used to understand the behaviour
of numerical methods – particularly related to their real-world application to industrial
problems.
The thesis begins by challenging some of the existing dogma surrounding computational fluid dynamics by evaluating the performance of high-order flux reconstruction.
First, the use of the primitive variables as an intermediary step in the construction of flux
terms is investigated. It is found that reducing the order of the flux function by using the
conserved rather than primitive variables has a substantial impact on the resolution of
the method. Critically, this is supported by a theoretical analysis, which shows that this
mechanism of error generation becomes increasing important to consider as the order of
accuracy increases.
Next, the analysis of Flux Reconstruction was extended by analytically and numerically exploring the impact of higher dimensionality and grid deformation. It is found
that both expanding and contracting grids – essential components of real-world domain
decomposition – can cause dispersion overshoot in two dimensions, but that FR appears
to suffer less that comparable Finite Difference approaches. Fully discrete analysis is then
used to show that, depending on the correction function, small perturbations in incidence
angle can cause large changes in group velocity. The same analysis is also used to theoretically demonstrate that Discontinuous Galerkin suffers less from dispersion error than
Huynh’s FR scheme – a phenomenon that has previously been observed experimentally,
but not explained theoretically.
This thesis concludes with the presentation of a robust theoretical underpinning for
determining stable correction functions for FR. Three new families of correction functions
are presented, and their properties extensively explored. An important theoretical finding
is introduced – that stable correction functions are not defined uniquely be a norm. As a
result, a generalised approach is presented, which is able to recover all previously defined
correction functions, but in some instances via a different norm to their original derivation.
This new super-family of correction functions shows considerable promise in increasing
temporal stability limits, reducing dispersion when fully discretised, and increasing the
rate of convergence.
Taken altogether, this thesis represents a considerable advance in the theoretical
characterisation and understanding of a numerical method – one which, it has been shown,
has enormous potential for forming the heart of future computational physics…
Subjects/Keywords: High-order methods; computational fluid dynamics; flux reconstruction; numerical analysis
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APA ·
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APA (6th Edition):
Trojak, W. (2020). Numerical Analysis of Flux Reconstruction. (Doctoral Dissertation). University of Cambridge. Retrieved from https://www.repository.cam.ac.uk/handle/1810/304614
Chicago Manual of Style (16th Edition):
Trojak, William. “Numerical Analysis of Flux Reconstruction.” 2020. Doctoral Dissertation, University of Cambridge. Accessed April 16, 2021.
https://www.repository.cam.ac.uk/handle/1810/304614.
MLA Handbook (7th Edition):
Trojak, William. “Numerical Analysis of Flux Reconstruction.” 2020. Web. 16 Apr 2021.
Vancouver:
Trojak W. Numerical Analysis of Flux Reconstruction. [Internet] [Doctoral dissertation]. University of Cambridge; 2020. [cited 2021 Apr 16].
Available from: https://www.repository.cam.ac.uk/handle/1810/304614.
Council of Science Editors:
Trojak W. Numerical Analysis of Flux Reconstruction. [Doctoral Dissertation]. University of Cambridge; 2020. Available from: https://www.repository.cam.ac.uk/handle/1810/304614
Uppsala University
10.
Hedlund, Erik.
High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles.
Degree: Division of Scientific Computing, 2016, Uppsala University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298754
We study noise from wind turbines while taking irregular terrain and non-constant atmosphere into consideration. We will show that simulating the distribution of 3D acoustic waves can be done by using only low frequencies, thus reducing the computational complexity significantly.
Subjects/Keywords: wave propagation; irregular terrain; high-order finite difference methods
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APA (6th Edition):
Hedlund, E. (2016). High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298754
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Hedlund, Erik. “High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles.” 2016. Thesis, Uppsala University. Accessed April 16, 2021.
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298754.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Hedlund, Erik. “High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles.” 2016. Web. 16 Apr 2021.
Vancouver:
Hedlund E. High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles. [Internet] [Thesis]. Uppsala University; 2016. [cited 2021 Apr 16].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298754.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Hedlund E. High-fidelity 3D acoustic simulations of wind turbines with irregular terrain and different atmospheric profiles. [Thesis]. Uppsala University; 2016. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298754
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Cambridge
11.
Trojak, William.
Numerical analysis of flux reconstruction.
Degree: PhD, 2020, University of Cambridge
URL: https://doi.org/10.17863/CAM.51695
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.805863
► High-order methods have become of increasing interest in recent years in computational physics. This is in part due to their perceived ability to, in some…
(more)
▼ High-order methods have become of increasing interest in recent years in computational physics. This is in part due to their perceived ability to, in some cases, reduce the computational overhead of complex problems through both an efficient use of computational resources and a reduction in the required degrees of freedom. One such high-order method in particular – Flux Reconstruction – is the focus of this thesis. This body of work relies and expands on the theoretical methods that are used to understand the behaviour of numerical methods – particularly related to their real-world application to industrial problems. The thesis begins by challenging some of the existing dogma surrounding computational fluid dynamics by evaluating the performance of high-order flux reconstruction. First, the use of the primitive variables as an intermediary step in the construction of flux terms is investigated. It is found that reducing the order of the flux function by using the conserved rather than primitive variables has a substantial impact on the resolution of the method. Critically, this is supported by a theoretical analysis, which shows that this mechanism of error generation becomes increasing important to consider as the order of accuracy increases. Next, the analysis of Flux Reconstruction was extended by analytically and numerically exploring the impact of higher dimensionality and grid deformation. It is found that both expanding and contracting grids – essential components of real-world domain decomposition – can cause dispersion overshoot in two dimensions, but that FR appears to suffer less that comparable Finite Difference approaches. Fully discrete analysis is then used to show that, depending on the correction function, small perturbations in incidence angle can cause large changes in group velocity. The same analysis is also used to theoretically demonstrate that Discontinuous Galerkin suffers less from dispersion error than Huynh’s FR scheme – a phenomenon that has previously been observed experimentally, but not explained theoretically. This thesis concludes with the presentation of a robust theoretical underpinning for determining stable correction functions for FR. Three new families of correction functions are presented, and their properties extensively explored. An important theoretical finding is introduced – that stable correction functions are not defined uniquely be a norm. As a result, a generalised approach is presented, which is able to recover all previously defined correction functions, but in some instances via a different norm to their original derivation. This new super-family of correction functions shows considerable promise in increasing temporal stability limits, reducing dispersion when fully discretised, and increasing the rate of convergence. Taken altogether, this thesis represents a considerable advance in the theoretical characterisation and understanding of a numerical method – one which, it has been shown, has enormous potential for forming the heart of future computational physics…
Subjects/Keywords: 530.15; High-order methods; computational fluid dynamics; flux reconstruction; numerical analysis
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APA (6th Edition):
Trojak, W. (2020). Numerical analysis of flux reconstruction. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.51695 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.805863
Chicago Manual of Style (16th Edition):
Trojak, William. “Numerical analysis of flux reconstruction.” 2020. Doctoral Dissertation, University of Cambridge. Accessed April 16, 2021.
https://doi.org/10.17863/CAM.51695 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.805863.
MLA Handbook (7th Edition):
Trojak, William. “Numerical analysis of flux reconstruction.” 2020. Web. 16 Apr 2021.
Vancouver:
Trojak W. Numerical analysis of flux reconstruction. [Internet] [Doctoral dissertation]. University of Cambridge; 2020. [cited 2021 Apr 16].
Available from: https://doi.org/10.17863/CAM.51695 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.805863.
Council of Science Editors:
Trojak W. Numerical analysis of flux reconstruction. [Doctoral Dissertation]. University of Cambridge; 2020. Available from: https://doi.org/10.17863/CAM.51695 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.805863
University of Texas – Austin
12.
Petrides, Socratis.
Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.
Degree: PhD, Computational Science, Engineering, and Mathematics, 2019, University of Texas – Austin
URL: http://dx.doi.org/10.26153/tsw/2153
► This dissertation focuses on the development of fast and efficient solution schemes for the simulation of challenging problems in wave propagation phenomena. In particular, emphasis…
(more)
▼ This dissertation focuses on the development of fast and efficient solution schemes for the simulation of challenging problems in wave propagation phenomena. In particular, emphasis is given on
high frequency acoustic and electromagnetic problems which are characterized by localized solutions. This kind of simulations are essential in various applications, such as ultrasonic testing, laser scanning and modeling of optical laser amplifiers.
In wave simulations, the computational cost of any numerical method, is directly related to the frequency. In the
high-frequency regime very fine meshes have to be used in
order to
satisfy the Nyquist criterion and overcome the pollution effect. This often leads to prohibitively expensive problems. Numerical
methods based on standard Galerkin discretizations lack pre-asymptotic discrete stability and therefore adaptive mesh refinement strategies are usually
inefficient. Additionally, the indefinite nature of the wave operator makes state of the art preconditioning techniques, such as multigrid, unreliable.
In this work, a promising alternative approach is followed within the framework of the discontinuous Petrov–Galerkin (DPG) method. The DPG method offers numerous advantages for our problems of interest. First and foremost, it offers mesh and frequency independent
discrete stability even in the pre-asymptotic region. This is made possible by computing, on the fly, an optimal test space as a function of the trial space. Secondly, it provides a built-in local error indicator that can be used to drive adaptive refinements. Combining these two properties
together, reliable adaptive refinement strategies are possible which can be initiated from very coarse meshes. Lastly, the DPG method can be viewed as a minimum residual method, and
therefore it always delivers symmetric (Hermitian) positive definite stiffness matrix. This is a desirable advantage when it comes to the design of iterative solution algorithms. Conjugate
Gradient based solvers can be employed which can be accelerated by domain decomposition (one- or multi- level) preconditioners for symmetric positive definite systems.
Driven by the aforementioned properties of the DPG method, an adaptive multigrid preconditioning technology is developed that is applicable for a wide range of boundary value problems. Unlike standard multigrid techniques, our preconditioner involves trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. Integration of the iterative solver within the DPG adaptive procedure turns out to be crucial in the simulation of
high frequency wave problems. A collection of numerical experiments for the solution of linear acoustics and Maxwell equations demonstrate the efficiency of this technology, where
under certain circumstances uniform convergence with respect to the mesh size, the polynomial
order and the frequency can be achieved. The construction is complemented with theoretical estimates for the condition number in the one-level setting.
Advisors/Committee Members: Demkowicz, Leszek (advisor), Biros, George (committee member), Bui-Thanh, Tan (committee member), Engquist, Bjorn (committee member), Gopalakrishnan, Jay (committee member), Simmons, Chris (committee member).
Subjects/Keywords: Multilevel iterative solvers; High frequency wave propagation; High order finite element methods; Domain decomposition preconditioners
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APA ·
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MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
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APA (6th Edition):
Petrides, S. (2019). Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2153
Chicago Manual of Style (16th Edition):
Petrides, Socratis. “Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed April 16, 2021.
http://dx.doi.org/10.26153/tsw/2153.
MLA Handbook (7th Edition):
Petrides, Socratis. “Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems.” 2019. Web. 16 Apr 2021.
Vancouver:
Petrides S. Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Apr 16].
Available from: http://dx.doi.org/10.26153/tsw/2153.
Council of Science Editors:
Petrides S. Adaptive multilevel solvers for the discontinuous Petrov–Galerkin method with an emphasis on high-frequency wave propagation problems. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/2153
13.
Li, Jizhou.
High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity.
Degree: PhD, Engineering, 2015, Rice University
URL: http://hdl.handle.net/1911/88087
► In my thesis, I formulate, analyze and implement high order discontinuous Galerkin methods for simulating miscible displacement in porous media. The analysis concerning the stability…
(more)
▼ In my thesis, I formulate, analyze and implement
high order discontinuous Galerkin
methods for simulating miscible displacement in porous media. The analysis concerning the stability and convergence under the minimal regularity assumption is established to provide theoretical foundations for using discontinuous Galerkin discretization to solve miscible displacement problems. The numerical experiments demonstrate the robustness and accuracy of the proposed
methods. The performance study for large scale simulations with highly heterogeneous porous media suggests strong scalability which indicates the efficiency of the numerical algorithm. The simulations performed using the algorithms for physically unstable flow show that higher
order methods proposed in thesis are more suitable for simulating such phenomenon than the commonly used cell-center finite volume method.
Advisors/Committee Members: Riviere, Beatrice M. (advisor), Symes, William (committee member), Hirasaki, George (committee member), Warburton, Timothy (committee member), Heinkenschloss, Matthias (committee member).
Subjects/Keywords: discontinuous Galerkin methods; miscible displacement; reservoir simulations; high performance computing; high order methods; viscous fingering; algebraic multigrid; domain decomposition
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APA ·
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MLA ·
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CSE |
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APA (6th Edition):
Li, J. (2015). High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity. (Doctoral Dissertation). Rice University. Retrieved from http://hdl.handle.net/1911/88087
Chicago Manual of Style (16th Edition):
Li, Jizhou. “High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity.” 2015. Doctoral Dissertation, Rice University. Accessed April 16, 2021.
http://hdl.handle.net/1911/88087.
MLA Handbook (7th Edition):
Li, Jizhou. “High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity.” 2015. Web. 16 Apr 2021.
Vancouver:
Li J. High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity. [Internet] [Doctoral dissertation]. Rice University; 2015. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1911/88087.
Council of Science Editors:
Li J. High order discontinuous Galerkin methods for simulating miscible displacement process in porous media with a focus on minimal regularity. [Doctoral Dissertation]. Rice University; 2015. Available from: http://hdl.handle.net/1911/88087
Iowa State University
14.
Zimmerman, Ben James.
A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling.
Degree: 2016, Iowa State University
URL: https://lib.dr.iastate.edu/etd/15181
► The impact threat of asteroids or comets, referred to as near-Earth objects (NEOs), is a growing concern to the global community. A NEO collision could…
(more)
▼ The impact threat of asteroids or comets, referred to as near-Earth objects (NEOs), is a growing concern to the global community. A NEO collision could have severe consequences, especially in highly populated regions. To combat this threat, several asteroid deflection strategies have been introduced, but computational modeling is needed to investigate the feasibility of such missions. To this end, an asteroid disruption software tool was built to handle the simulation of multiple disruption techniques, namely high-energy explosives and kinetic-energy impactors, and to investigate the feasibility and effectiveness of these approaches. In addition, the software is intended to use graphics processing units (GPUs) as the primary computational resource rather than central processing units (CPUs). While GPUs are quickly becoming an alternative computing platform for numerical simulations, it is not clear which numerical schemes provide the highest computational efficiency for different problem types.
The numerical accuracies and computational work of several numerical methods are compared using GPU computing implementation. The Correction Procedure via Reconstruction (CPR), Discontinuous Galerkin (DG), Nodal Discontinuous Galerkin (NDG), Spectral Difference (SD), and Finite Volume (FV) methods are investigated for smooth and discontinuous problems to determine the most efficient method to apply towards asteroid disruption simulations. The computational time to reach a set error criteria and total time to compute solutions are compared across the methods. It is shown that while FV methods can produce solutions with the lowest computation time for discontinuous problems, they produce larger errors for smooth problems at the same order of accuracy. The SD method illustrates an excellent trade-off in terms of error and total work, computing both smooth and discontinuous problems faster than most other methods while providing low error norms.
From the aforementioned study, the SD method is applied to multifluid modeling for asteroid disruption applications. In order to model the multiple material phases associated with the problem, a Diffused-Interface Method (DIM) approach is integrated into the SD method (SD-DIM). This allows high-order solution reconstructions for problems containing multi-material interactions, where different equations of states define each material. In addition, a damage model is developed to simulate asteroid fracturing based on material phase changes. This results in a novel GPU-based high-order SD-DIM computational tool to explore the complex problem of asteroid fragmentation and pulverization. Several asteroid disruption simulations are completed, including kinetic-energy impactors, multi-kinetic energy impactor systems, and nuclear options. Results illustrate the benefits of using a multi-kinetic energy system when compared to a single impactor system for non-nuclear options. The effectiveness of nuclear options is also observed, where complete target destruction is shown.
Subjects/Keywords: Aerospace Engineering; Asteroid Disruption; GPU CUDA; High-order methods; Hypervelocity impact; Multifluid modeling; Aerospace Engineering
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APA (6th Edition):
Zimmerman, B. J. (2016). A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/15181
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Zimmerman, Ben James. “A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling.” 2016. Thesis, Iowa State University. Accessed April 16, 2021.
https://lib.dr.iastate.edu/etd/15181.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zimmerman, Ben James. “A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling.” 2016. Web. 16 Apr 2021.
Vancouver:
Zimmerman BJ. A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling. [Internet] [Thesis]. Iowa State University; 2016. [cited 2021 Apr 16].
Available from: https://lib.dr.iastate.edu/etd/15181.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zimmerman BJ. A GPU-accelerated high-order multiphase computational tool for asteroid fragmentation and pulverization modeling. [Thesis]. Iowa State University; 2016. Available from: https://lib.dr.iastate.edu/etd/15181
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Iowa State University
15.
Gao, Haiyang.
Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations.
Degree: 2011, Iowa State University
URL: https://lib.dr.iastate.edu/etd/12248
► A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is…
(more)
▼ A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin (DG), staggered grid, spectral volume (SV), and spectral difference (SD).
The approach is then extended to diffusion equation and Navier-Stokes equations. In the discretization of the diffusion terms, the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches are used. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh.
The current work also includes a study of high-order curve boundaries representations. A new boundary representation based on the Bezier curve is then developed and analyzed, which is shown to have several advantages for complicated geometries.
To further enhance the efficiency, the capability of h/p mesh adaptation is developed for the CPR solver. The adaptation is driven by an efficient multi-p a posteriori error estimator. P-adaptation is applied to smooth regions of the flow field while h-adaptation targets the non-smooth regions, identified by accuracy-preserving TVD marker. Several numerical tests are presented to demonstrate the capability of the technique.
Subjects/Keywords: curved boundary; differential formulation; discontinuous Galerkin; high-order methods; h/p adaptation; Aerospace Engineering
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APA (6th Edition):
Gao, H. (2011). Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/12248
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Gao, Haiyang. “Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations.” 2011. Thesis, Iowa State University. Accessed April 16, 2021.
https://lib.dr.iastate.edu/etd/12248.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Gao, Haiyang. “Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations.” 2011. Web. 16 Apr 2021.
Vancouver:
Gao H. Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations. [Internet] [Thesis]. Iowa State University; 2011. [cited 2021 Apr 16].
Available from: https://lib.dr.iastate.edu/etd/12248.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Gao H. Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations. [Thesis]. Iowa State University; 2011. Available from: https://lib.dr.iastate.edu/etd/12248
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Colorado State University
16.
Owen, Landon.
Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A.
Degree: PhD, Mechanical Engineering, 2019, Colorado State University
URL: http://hdl.handle.net/10217/195423
► Accurate computational modeling of reacting flows is necessary to improve the design combustion efficiency and emission reduction in combustion devices, such as gas turbine engines.…
(more)
▼ Accurate computational modeling of reacting flows is necessary to improve the design combustion efficiency and emission reduction in combustion devices, such as gas turbine engines. Combusting flows consists of a variety of phenomena including fluid mixing, chemical kinetics, turbulence-chemistry interacting dynamics, and heat and mass transfer. The scales associated with these range from atomic scales up to continuum scales at device level. Therefore, combusting flows are strongly nonlinear and require multiphysics and multiscale modeling. This research employs a fourth-
order finite-volume method and leverages increasing gains in modern computing power to achieve
high-fidelity modeling of flow characteristics and combustion dynamics. However, it is challenging to ensure that computational models are accurate, stable, and efficient due to the multiscale and multiphysics nature of combusting flows. Therefore, the goal of this research is to create a robust,
high-
order finite-volume algorithm on mapped domains with adaptive mesh refinement to solve compressible combustion problems in relatively complex geometries on parallel computing architecture. There are five main efforts in this research. The first effort is to extend the existing algorithm to solve the compressible Navier-Stokes equations on mapped domains by implementing the fourth-
order accurate viscous discretization operators. The second effort is to incorporate the species transport equations and chemical kinetics into the solver to enable combustion modeling. The third effort is to ensure stability of the algorithm for combustion simulations over a wide range of speeds. The fourth effort is to ensure all new functionality utilizes the parallel adaptive mesh refinement infrastructure to achieve efficient computations on
high-performance computers. The final goal is to utilize the algorithm to simulate a range of flow problems, including a multispecies flow with Mach reflection, multispecies mixing flow through a planar burner, and oblique detonation waves over a wedge. This research produces a verified and validated, fourth-
order finite-volume algorithm for solving thermally perfect, compressible, chemically reacting flows on mapped domains that are adaptively refined and represent moderately complex geometries. In the future, the framework established in this research will be extended to model reactive flows in gas turbine combustors.
Advisors/Committee Members: Gao, Xinfeng (advisor), Guzik, Stephen (committee member), Marchese, Anthony (committee member), Estep, Donald (committee member).
Subjects/Keywords: computational fluid dynamics; high-order finite-volume methods; detonations; compressible reacting flows
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APA (6th Edition):
Owen, L. (2019). Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/195423
Chicago Manual of Style (16th Edition):
Owen, Landon. “Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A.” 2019. Doctoral Dissertation, Colorado State University. Accessed April 16, 2021.
http://hdl.handle.net/10217/195423.
MLA Handbook (7th Edition):
Owen, Landon. “Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A.” 2019. Web. 16 Apr 2021.
Vancouver:
Owen L. Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A. [Internet] [Doctoral dissertation]. Colorado State University; 2019. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/10217/195423.
Council of Science Editors:
Owen L. Fourth-order solution-adaptive finite-volume algorithm for compressible reacting flows on mapped domains, A. [Doctoral Dissertation]. Colorado State University; 2019. Available from: http://hdl.handle.net/10217/195423
Colorado School of Mines
17.
Morgenstern, Charles O.
High-order high-performance computing algorithms for wave propagation in heterogeneous media.
Degree: PhD, Applied Mathematics and Statistics, 2016, Colorado School of Mines
URL: http://hdl.handle.net/11124/170316
► Understanding the propagation of waves using computer models is important for several applications. Major challenges for developing efficient wave propagation computer models include incorporating heterogeneous…
(more)
▼ Understanding the propagation of waves using computer models is important for several applications. Major challenges for developing efficient wave propagation computer models include incorporating heterogeneous and unbounded wave propagation media, and
high-frequency data. Such models lead to very large and poorly conditioned indefinite linear systems. The main focus of this thesis is to address these challenges through several mathematical and
high-performance computing techniques. Our novel algorithms include developing and implementing unbounded heterogeneous media models using a hybrid of finite element and boundary element
methods (FEM/BEMs). For incorporating heterogeneous media,
high-frequency input data, and hybrid models, large scale simulations are needed in conjunction with iterative
methods for indefinite systems. We develop efficient computer models through innovative preconditioned iterative
high-
order FEMs. Our implementation includes multigrid and domain decomposition algorithms, and multiple- and
high-frequency simulations in two- and three-dimensional heterogeneous media with non-smooth and curved boundaries. Indefiniteness is a major computational bottleneck for wave propagation models that have been investigated for several decades. In addition to our efficient
methods for the standard indefinite systems, we develop, analyze, and implement a new class of sign-definite
high-
order preconditioned wave propagation computer models. Our sign-definite iterative models require a small number of iterations which is independent of the frequency of the wave propagation. We demonstrate our many novel algorithms developed in this thesis using
high-performance parallel computing implementations.
Advisors/Committee Members: Ganesh, Mahadevan (advisor), Tilton, Nils (committee member), Tenorio, Luis (committee member), Porter, Aaron T. (committee member).
Subjects/Keywords: boundary element method; finite element method; high-order; indefinite systems; iterative methods; wave propagation
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APA (6th Edition):
Morgenstern, C. O. (2016). High-order high-performance computing algorithms for wave propagation in heterogeneous media. (Doctoral Dissertation). Colorado School of Mines. Retrieved from http://hdl.handle.net/11124/170316
Chicago Manual of Style (16th Edition):
Morgenstern, Charles O. “High-order high-performance computing algorithms for wave propagation in heterogeneous media.” 2016. Doctoral Dissertation, Colorado School of Mines. Accessed April 16, 2021.
http://hdl.handle.net/11124/170316.
MLA Handbook (7th Edition):
Morgenstern, Charles O. “High-order high-performance computing algorithms for wave propagation in heterogeneous media.” 2016. Web. 16 Apr 2021.
Vancouver:
Morgenstern CO. High-order high-performance computing algorithms for wave propagation in heterogeneous media. [Internet] [Doctoral dissertation]. Colorado School of Mines; 2016. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/11124/170316.
Council of Science Editors:
Morgenstern CO. High-order high-performance computing algorithms for wave propagation in heterogeneous media. [Doctoral Dissertation]. Colorado School of Mines; 2016. Available from: http://hdl.handle.net/11124/170316
University of Toronto
18.
Barrera, Roberto Armenta.
The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations.
Degree: 2012, University of Toronto
URL: http://hdl.handle.net/1807/33908
► The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of…
(more)
▼ The principle of coordinate invariance states that all physical laws must be formulated in a mathematical form that is independent of the geometrical properties of any particular coordinate system. Embracing this principle is the key to understand how to systematically incorporate curved material interfaces into a numerical solution of Maxwell’s equations. This dissertation describes how to generate a coordinate invariant representation of Maxwell’s equations in differential form, and it demonstrates why employing such representation is crucial to the development of robust finite-difference discretisations with consistent global error properties. As part of this process, two original contributions are presented that address the issue of constructing finite-difference approximations at the locations of material interfaces. The first contribution is a domain-decomposition procedure to enforce the tangential field continuity conditions with a second-order local truncation error that can be applied in 2-D or 3-D. The second contribution is a similar domain-decomposition procedure that enforces the tangential field continuity conditions with a local truncation of order 2L—where L is an integer greater or equal to one—but that can only be applied in 1-D. To conclude, the dissertation also describes the interesting connection that exists between the use of a coordinate invariant representation of Maxwell’s equations to design artificial materials and the use of the same representation to model curved material interfaces in a finite-difference discretisation.
PhD
Advisors/Committee Members: Sarris, Costas D., Electrical and Computer Engineering.
Subjects/Keywords: numerical techniques; finite-difference methods; material boundaries; material interfaces; artificial materials; metamaterials; FDTD; high-order methods; 0544; 0607; 0405
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APA (6th Edition):
Barrera, R. A. (2012). The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations. (Doctoral Dissertation). University of Toronto. Retrieved from http://hdl.handle.net/1807/33908
Chicago Manual of Style (16th Edition):
Barrera, Roberto Armenta. “The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations.” 2012. Doctoral Dissertation, University of Toronto. Accessed April 16, 2021.
http://hdl.handle.net/1807/33908.
MLA Handbook (7th Edition):
Barrera, Roberto Armenta. “The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations.” 2012. Web. 16 Apr 2021.
Vancouver:
Barrera RA. The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations. [Internet] [Doctoral dissertation]. University of Toronto; 2012. [cited 2021 Apr 16].
Available from: http://hdl.handle.net/1807/33908.
Council of Science Editors:
Barrera RA. The Principle of Coordinate Invariance and the Modelling of Curved Material Interfaces in Finite-difference Discretisations of Maxwell's Equations. [Doctoral Dissertation]. University of Toronto; 2012. Available from: http://hdl.handle.net/1807/33908
Temple University
19.
Zhou, Dong.
High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations.
Degree: PhD, 2014, Temple University
URL: http://digital.library.temple.edu/u?/p245801coll10,295839
► Mathematics
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional…
(more)
▼ Mathematics
Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time.
Temple University – Theses
Advisors/Committee Members: Seibold, Benjamin;, Klapper, Isaac, Szyld, Daniel, Rosales, Rodolfo R.;.
Subjects/Keywords: Mathematics;
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APA (6th Edition):
Zhou, D. (2014). High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations. (Doctoral Dissertation). Temple University. Retrieved from http://digital.library.temple.edu/u?/p245801coll10,295839
Chicago Manual of Style (16th Edition):
Zhou, Dong. “High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations.” 2014. Doctoral Dissertation, Temple University. Accessed April 16, 2021.
http://digital.library.temple.edu/u?/p245801coll10,295839.
MLA Handbook (7th Edition):
Zhou, Dong. “High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations.” 2014. Web. 16 Apr 2021.
Vancouver:
Zhou D. High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations. [Internet] [Doctoral dissertation]. Temple University; 2014. [cited 2021 Apr 16].
Available from: http://digital.library.temple.edu/u?/p245801coll10,295839.
Council of Science Editors:
Zhou D. High-order numerical methods for pressure Poisson equation reformulations of the incompressible Navier-Stokes equations. [Doctoral Dissertation]. Temple University; 2014. Available from: http://digital.library.temple.edu/u?/p245801coll10,295839
Penn State University
20.
Zheng, Bin.
Finite Element Approximations of High Order Partial Differential Equations.
Degree: 2008, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/8776
► Developing accurate and efficient numerical approximations of solutions of high order partial differential equations (PDEs) is a challenging research topic. In this dissertation, we study…
(more)
▼ Developing accurate and efficient numerical approximations of solutions of
high order partial differential equations (PDEs) is a challenging research topic.
In this dissertation, we study finite element approximations of
high order PDEs that arise in many physics and engineering applications.
A common method of solving a
high order PDE is to split it into a system of lower
order equations. By carefully studying the biharmonic equation with different types of boundary conditions, we are able to justify the fact that the lower
order system of equations and the original problem may have different solutions. Our analysis shows that direct discretizations are much better suited for the numerical solution of
high order problems.
We construct two finite elements to directly discretize
high order equations arising from magnetohydrodynamics (MHD) models. These elements provide nonconforming approximations for which the number of degrees of freedom is much smaller than that of a conforming method. The inter-element continuity is only imposed along the tangential directions which is appropriate for the approximation of the magnetic field. A detailed construction of basis functions for the new elements is given, and we also prove that these finite element approximations converge for a model problem containing both second
order and fourth
order terms.
Another important property of
high order PDEs that model physical phenomena in material sciences, fluid mechanics and plasma physics is that they often involve different time and spatial scales. The solutions exhibit sharp interfaces, such as shocks, current sheets and other singularities. Adaptive mesh refinement techniques are therefore crucial for reliable numerical computations of
high order problems. We develop a post-processing derivative recovery scheme and a posteriori error estimates that can be used in local adaptive mesh refinement. A nice feature of the scheme is that it is independent of the PDE and a single implementation can be used to solve many different problems.
Advisors/Committee Members: Jinchao Xu, Committee Chair/Co-Chair, Chun Liu, Committee Member, Eric M Mockensturm, Committee Member, Victor Nistor, Committee Member, Ludmil Tomov Zikatanov, Committee Member.
Subjects/Keywords: finite element methods; high order partial differential equations; magnetohydrodynamics
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APA (6th Edition):
Zheng, B. (2008). Finite Element Approximations of High Order Partial Differential Equations. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/8776
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Zheng, Bin. “Finite Element Approximations of High Order Partial Differential Equations.” 2008. Thesis, Penn State University. Accessed April 16, 2021.
https://submit-etda.libraries.psu.edu/catalog/8776.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Zheng, Bin. “Finite Element Approximations of High Order Partial Differential Equations.” 2008. Web. 16 Apr 2021.
Vancouver:
Zheng B. Finite Element Approximations of High Order Partial Differential Equations. [Internet] [Thesis]. Penn State University; 2008. [cited 2021 Apr 16].
Available from: https://submit-etda.libraries.psu.edu/catalog/8776.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Zheng B. Finite Element Approximations of High Order Partial Differential Equations. [Thesis]. Penn State University; 2008. Available from: https://submit-etda.libraries.psu.edu/catalog/8776
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Penn State University
21.
Ferrer, Rodolfo Miguel.
An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids.
Degree: 2010, Penn State University
URL: https://submit-etda.libraries.psu.edu/catalog/10500
► An extension of the Arbitrarily High-Order Transport Method of the Characteristic type to three-dimensional unstructured tetrahedral grids is proposed in this work which resolves the…
(more)
▼ An extension of the Arbitrarily
High-
Order Transport Method of the Characteristic type to three-dimensional unstructured tetrahedral grids is proposed in this work which resolves the difficulties encountered in the earlier formulation of the method. A thorough literature review is presented of the development of characteristic
methods as a specific class of spatial discretization to the discrete-ordinates approximation of the stationary transport equation. A classical derivation of the Arbitrarily
High-
Order Transport Method of the Characteristic Type for Unstructured Grids (AHOT-C-UG) is performed, which is based on a consistent generalization of lower-
order short characteristic
methods in structured grids. Novel techniques, such as coordinate transformations and series expansions of spatial moments, are introduced in
order to avoid previous difficulties regarding computational precision and the treatment of internal voids. In addition, the arbitrary-
order characteristic relation is re-derived in a form which satisfies emph{exactly} the arbitrary-
order balance equation. The consequences of the equivalence are twofold: it provides an exact relation that is numerically stable as the computational cells become optically thin, and it underscores the fact that the characteristic relation conserves the local balance of all computed spatial moments of the particle population, which is an important property of good spatial discretizations to the transport equation. Furthermore, the AHOT-C-UG approach is subsequently reintroduced as a Discontinuous Petrov-Galerkin projection, which allows us to bridge the gap between characteristic
methods that are consistent with AHOT-C-UG and general finite element
methods by providing a common setting from the point of view of variational analysis. Remaining mathematical and computational challenges regarding the AHOT-C-UG approach are noted and practical solutions to these issues are suggested. A rudimentary performance model of the method is introduced in
order to address practical concerns regarding computational resources and runtime performance. Numerical results are shown which verify the validity of the performance model. In addition, the expected behavior of the method's convergence rate, based on the behavior of the error with respect to mesh refinement for a specified set of spatial expansion orders, is verified by performing a set of numerical experiments. Finally, a set of computational benchmarks are solved in
order to show that the formalism can be used to analyze realistic radiation transport problems.
Advisors/Committee Members: Kostadin Nikolov Ivanov, Dissertation Advisor/Co-Advisor, Kostadin Nikolov Ivanov, Committee Chair/Co-Chair, Yousry Y Azmy, Committee Chair/Co-Chair, Seungjin Kim, Committee Member, Deborah A Levin, Committee Member, David W Nigg, Committee Member, Ronaldo H Szilard, Committee Member.
Subjects/Keywords: Transport Theory; Discrete Ordinates; Characteristic Methods; High Order
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CSE |
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APA (6th Edition):
Ferrer, R. M. (2010). An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/10500
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Ferrer, Rodolfo Miguel. “An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids.” 2010. Thesis, Penn State University. Accessed April 16, 2021.
https://submit-etda.libraries.psu.edu/catalog/10500.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Ferrer, Rodolfo Miguel. “An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids.” 2010. Web. 16 Apr 2021.
Vancouver:
Ferrer RM. An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids. [Internet] [Thesis]. Penn State University; 2010. [cited 2021 Apr 16].
Available from: https://submit-etda.libraries.psu.edu/catalog/10500.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Ferrer RM. An Arbitrarily High Order Transport Method of the Characteristic Type for Unstructured Tetrahedral Grids. [Thesis]. Penn State University; 2010. Available from: https://submit-etda.libraries.psu.edu/catalog/10500
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Brigham Young University
22.
Grundvig, Dane Scott.
High Order Numerical Methods for Problems in Wave Scattering.
Degree: MS, 2020, Brigham Young University
URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9617&context=etd
► Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high…
(more)
▼ Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Details and results from an extension to heterogeneous media are also included. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the proposed method. A novel local high order ABC for elastic waves based on farfield expansions is constructed and preliminary results applying it to elastic scattering problems are presented.
Subjects/Keywords: acoustic scattering; elastic scattering; Helmholtz equation; high order numerical methods; variable wave number; heterogeneous media; deferred corrections; Physical Sciences and Mathematics
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APA (6th Edition):
Grundvig, D. S. (2020). High Order Numerical Methods for Problems in Wave Scattering. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9617&context=etd
Chicago Manual of Style (16th Edition):
Grundvig, Dane Scott. “High Order Numerical Methods for Problems in Wave Scattering.” 2020. Masters Thesis, Brigham Young University. Accessed April 16, 2021.
https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9617&context=etd.
MLA Handbook (7th Edition):
Grundvig, Dane Scott. “High Order Numerical Methods for Problems in Wave Scattering.” 2020. Web. 16 Apr 2021.
Vancouver:
Grundvig DS. High Order Numerical Methods for Problems in Wave Scattering. [Internet] [Masters thesis]. Brigham Young University; 2020. [cited 2021 Apr 16].
Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9617&context=etd.
Council of Science Editors:
Grundvig DS. High Order Numerical Methods for Problems in Wave Scattering. [Masters Thesis]. Brigham Young University; 2020. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=9617&context=etd
23.
GALINDEZ RAMIREZ, Gustavo.
Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
.
Degree: 2018, Universidade Federal de Pernambuco
URL: https://repositorio.ufpe.br/handle/123456789/33064
► The study and development of high resolution numerical approximations for the modeling and simulation of multiphase flows in petroleum reservoirs is still a challenge, from…
(more)
▼ The study and development of
high resolution numerical approximations for the modeling and simulation of multiphase flows in petroleum reservoirs is still a challenge, from the computational viewpoint, due to the difficulties posed by some physical features such as heterogeneity and anisotropy of the medium, that are of paramount importance in this class of applications. Several
methods have been proposed in the past that are based on FD (Finite-Difference), FV (Finite-Volume) or FE (Finite-Element). These
methods, in their classical formulations, are of low
order of approximation and suffer excessive smearing at saturation front introducing error into the numerical solution. These deficiencies can be mitigated or suppressed using highresolution
methods such as the k-exact or ENO (Essentially non-Oscillatory) FV
methods, which require large stencils to reconstruct
high order polynomial within a control volume, resulting in an increase of the storage requirements and computational cost. On the other hand, over the last decades DG (Discontinuous Galerkin), SV (Spectral Volume), SD (Spectral Difference) and FR (Flux Reconstruction)/CPR (Correction Procedure via Reconstruction)
methods were developed, which can achieve
high order accuracy via a compact stencil consisting of the current cell and its immediate neighbors. In addition, the FR/CPR recovery simplified versions of nodal DG, SV and SD
methods by choosing an adequate polynomial reconstruction function, whose coefficients are preprocessed and stored. The focus of this work is to investigate and to apply a very
high resolution CPR method for the discretization of the saturation equation, which is generally advection-dominated and that results from the modeling of the 2-D Oil-Water displacement through porous formations. In
order to suppress numerical oscillations (under/over shoots) near shocks that are typical in higher
order schemes, and handing the
high accuracy in smooth regions of the solution a hierarchical multi-dimensional limiting strategy (MLP) is used in the reconstruction stage. The integration in time is carried out using a third-
order Runge-Kutta method. To solve the pressure equation a non-orthodox cell centered MPFA-D (Multipoint Flux Approximation-Diamond type) finite volume method is employed. In
order to properly couple the MPFA-D method with the CPR formulation, it is necessary to obtain an adequate velocity reconstruction throughout the control volumes of the mesh. Because the cell-centered finite volume method naturally delivers fluxes across cell faces that belong to the primal grid, a reconstruction operator based on the lowest Raviart-Thomas interpolation functions and the Piola transformation is built, to get the complete knowledge of conservative velocity field throughout the domain. The reconstruction operator receives, as input, the density fluxes across control volume faces and returns the point-wise values of velocity anywhere within the cell. Finally, the coupling of the pressure-saturation system of equations is carried out using a…
Advisors/Committee Members: LYRA, Paulo Roberto Maciel (advisor), CARVALHO, Darlan Karlo Elisiário de (advisor), http://lattes.cnpq.br/6568615406054840 (advisor).
Subjects/Keywords: Engenharia Mecânica;
High order methods;
CPR;
MLP;
MPFA-D;
IMPES;
Raviart-Thomas interpolation;
The Piola trasformation;
Twophase flows in porous media
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APA ·
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APA (6th Edition):
GALINDEZ RAMIREZ, G. (2018). Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
. (Doctoral Dissertation). Universidade Federal de Pernambuco. Retrieved from https://repositorio.ufpe.br/handle/123456789/33064
Chicago Manual of Style (16th Edition):
GALINDEZ RAMIREZ, Gustavo. “Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
.” 2018. Doctoral Dissertation, Universidade Federal de Pernambuco. Accessed April 16, 2021.
https://repositorio.ufpe.br/handle/123456789/33064.
MLA Handbook (7th Edition):
GALINDEZ RAMIREZ, Gustavo. “Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
.” 2018. Web. 16 Apr 2021.
Vancouver:
GALINDEZ RAMIREZ G. Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
. [Internet] [Doctoral dissertation]. Universidade Federal de Pernambuco; 2018. [cited 2021 Apr 16].
Available from: https://repositorio.ufpe.br/handle/123456789/33064.
Council of Science Editors:
GALINDEZ RAMIREZ G. Numerical simulation of two-phase flow in petroleum reservoirs using high-order CPR method coupled to a non-orthodox MPFA-D finite volume scheme
. [Doctoral Dissertation]. Universidade Federal de Pernambuco; 2018. Available from: https://repositorio.ufpe.br/handle/123456789/33064
24.
Barrau, Nelly.
Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization.
Degree: Docteur es, Mathématiques appliquées, 2013, Pau
URL: http://www.theses.fr/2013PAUU3025
► Cette thèse porte sur la généralisation de la méthode NXFEM proposée par A. et P. Hansbo pour le problème d’interface elliptique. La modélisation et simulation…
(more)
▼ Cette thèse porte sur la généralisation de la méthode NXFEM proposée par A. et P. Hansbo pour le problème d’interface elliptique. La modélisation et simulation numérique d’écoulements dans des domaines fracturés sont au coeur de nombreuses applications, telles que le milieu pétrolier (modélisation de réservoirs, présence de failles, propagation d’un signal, repérage de couches), l’aérospatiale (problème de chocs, de rupture), en génie civil (fissuration du béton), mais également dans la biologie cellulaire (déformation des globules rouges). En outre, de nombreux projets de recherche nécessitent le développement des méthodes robustes pour la prise en compte de singularités, ce qui fait partie des motivations et des objectifs de l'équipe Concha, ainsi que de cette thèse. Une modification de cette méthode a tout d’abord été proposée afin d’obtenir la robustesse à la fois par rapport à la géométrie du maillage coupé par l’interface et par rapport aux paramètres de diffusion. Nous nous sommes ensuite intéressés à sa généralisation à tout type de maillages 2D-3D (triangles, quadrilatères, tétraèdres, hexaèdres), et pour tout type d’éléments finis (conformes, non conformes, Galerkin discontinus) pour des interfaces planes et courbes. Les applications ont été orientées vers des problèmes d’écoulements en milieux poreux fracturés : adaptation de la méthode NXFEM à la résolution d’un modèle asymptotique de failles, à des problèmes instationnaires, de transports, ou encore à des domaines multi-fracturés.
This thesis focuses on the generalization of the NXFEM method proposed by A. and P. Hansbo for elliptic interface problem. Numerical modeling and simulation of flow in fractured media are at the heart of many applications, such as petroleum and porous media (reservoir modeling, presence of faults, signal propagation, identification of layers ...), aerospace (problems of shock, rupture), civil engineering (concrete cracking), but also in cell biology (deformation of red blood cells). In addition, many research projects require the development of robust methods for the consideration of singularities, which is one of the motivations and objectives of the Concha team and of this thesis. First a modification of this method was proposed to obtain a robust method not only with respect to the mesh-interface geometry, but also with respect to the diffusion parameters. We then looked to its generalization to any type of 2D-3D meshes (triangles, quadrilaterals, tetrahedra, hexahedra), and for any type of finites elements (conforming, nonconforming, Galerkin discontinuous) for plane and curved interfaces. The applications have been referred to the flow problems in fractured porous media : adaptation of NXFEM method to solve an asymptotic model of faults, to unsteady problems, transport problems, or to multi-fractured domains.
Advisors/Committee Members: Luce, Robert (thesis director).
Subjects/Keywords: NXFEM; Généralisation à l’ordre supérieur; Maillages 2D-3D; Méthodes adaptatives; NXFEM; High-order generalization; 2D-3D meshes; Adaptive methods
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APA (6th Edition):
Barrau, N. (2013). Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization. (Doctoral Dissertation). Pau. Retrieved from http://www.theses.fr/2013PAUU3025
Chicago Manual of Style (16th Edition):
Barrau, Nelly. “Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization.” 2013. Doctoral Dissertation, Pau. Accessed April 16, 2021.
http://www.theses.fr/2013PAUU3025.
MLA Handbook (7th Edition):
Barrau, Nelly. “Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization.” 2013. Web. 16 Apr 2021.
Vancouver:
Barrau N. Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization. [Internet] [Doctoral dissertation]. Pau; 2013. [cited 2021 Apr 16].
Available from: http://www.theses.fr/2013PAUU3025.
Council of Science Editors:
Barrau N. Généralisation de la méthode Nitsche XFEM pour la discrétisation de problèmess d'interface elliptiques : NXFEM generalization for elliptic interface problems discretization. [Doctoral Dissertation]. Pau; 2013. Available from: http://www.theses.fr/2013PAUU3025
Uppsala University
25.
Almquist, Martin.
Numerical wave propagation in large-scale 3-D environments.
Degree: Division of Scientific Computing, 2012, Uppsala University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171958
► High-order accurate finite difference methods have been applied to the acoustic wave equation in discontinuous media and curvilinear geometries, using the SBP-SAT method. Strict…
(more)
▼ High-order accurate finite difference methods have been applied to the acoustic wave equation in discontinuous media and curvilinear geometries, using the SBP-SAT method. Strict stability is shown for the 2-D wave equation with general boundary conditions. The fourth-order accurate method for the 3-D wave equation has been implemented in C and parallelized using MPI. The implementation has been verified against an analytical solution and runs efficiently on a large number of processors.
Subjects/Keywords: high-order finite difference methods; wave propagation; numerical stability; parallel efficiency; Other Computer and Information Science; Annan data- och informationsvetenskap
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APA (6th Edition):
Almquist, M. (2012). Numerical wave propagation in large-scale 3-D environments. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171958
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Almquist, Martin. “Numerical wave propagation in large-scale 3-D environments.” 2012. Thesis, Uppsala University. Accessed April 16, 2021.
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171958.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Almquist, Martin. “Numerical wave propagation in large-scale 3-D environments.” 2012. Web. 16 Apr 2021.
Vancouver:
Almquist M. Numerical wave propagation in large-scale 3-D environments. [Internet] [Thesis]. Uppsala University; 2012. [cited 2021 Apr 16].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171958.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Almquist M. Numerical wave propagation in large-scale 3-D environments. [Thesis]. Uppsala University; 2012. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-171958
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Cincinnati
26.
Wukie, Nathan A.
A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications.
Degree: PhD, Engineering and Applied Science: Aerospace
Engineering, 2018, University of Cincinnati
URL: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045
► Numerical methods for computational physics have been applied for many years in the fields of turbomachinery and acoustics. The computational approach to addressing problems in…
(more)
▼ Numerical
methods for computational physics have been
applied for many years in the fields of turbomachinery and
acoustics. The computational approach to addressing problems in
these fields has strongly influenced improvements in performance
and advancements in understanding for the systems and physical
processes that govern such applications. Particularly within the
turbomachinery community, the spectrum of numerical
methods being
applied is dominated by second-
order accurate finite-volume and
finite-difference discretizations of the governing equations. These
have been quite successful and their robustness has been important
in their adoption within industrial engineering as tools for design
and analysis. At the same time, such approaches are very
dissipative and require dense computational grids to resolve sharp
features and capture wave propagation. As problems become more
complex and inter-related, the numerical methodologies for analysis
tools that are used to address such problems and inform solutions
must improve in their fidelity, accuracy, and mathematical rigor.At
the same time,
high-
order finite-element
methods have experienced
significant attention in the computational fluid dynamics community
for their mathematical formalism, localized approach for obtaining
high-
order accuracy, and amenability to adaptation of the numerical
grid and accuracy of the numerical approximation. The challenges of
such approaches are to achieve efficiency and stability for the
numerical method. The result of many research efforts in this area
has pushed the applicability of
high-
order finite-element
methods
into many fields and they are approaching the point where they
might soon find routine application to industrial problems for
engineering design and analysis. This dissertation details the
development and application of an implicit discontinuous Galerkin
method to applications in turbomachinery and acoustics. This is
carried out for the purpose of advancing the applicability of the
discontinuous Galerkin method to problems in these fields. A
selection of the developments included in this work include a study
on the efficiency of automatic differentiation for the
discontinuous Galerkin method, adoption of a new approach for
computing distance fields based on solving a p-Poisson equation,
the development of a new adiabatic no-slip boundary condition for
moving walls, and the development of implicit nonlocal
nonreflecting boundary conditions along with a new stabilizing
correction that significantly improves their efficiency and
robustness. Mixing-plane interfaces for turbomachinery applications
were also developed for the first time within a discontinuous
Galerkin discretization. Finally, the numerical method that was
created in the context of this work was applied to several
turbomachinery problems. These problems include steady,
Reynolds-Averaged Navier-Stokes (RANS) calculations for a
two-dimensional stator, a three-dimensional stator, and a quasi
three-dimensional 1.5 stage turbine using nonreflecting
mixing-plane…
Advisors/Committee Members: Orkwis, Paul (Committee Chair).
Subjects/Keywords: Aerospace Materials; High-order methods; Computational Fluid Dynamics; discontinuous Galerkin; Nonreflecting boundary conditions; Turbomachinery; Finite-elements
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APA ·
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MLA ·
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APA (6th Edition):
Wukie, N. A. (2018). A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications. (Doctoral Dissertation). University of Cincinnati. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045
Chicago Manual of Style (16th Edition):
Wukie, Nathan A. “A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications.” 2018. Doctoral Dissertation, University of Cincinnati. Accessed April 16, 2021.
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045.
MLA Handbook (7th Edition):
Wukie, Nathan A. “A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications.” 2018. Web. 16 Apr 2021.
Vancouver:
Wukie NA. A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications. [Internet] [Doctoral dissertation]. University of Cincinnati; 2018. [cited 2021 Apr 16].
Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045.
Council of Science Editors:
Wukie NA. A Discontinuous Galerkin Method for Turbomachinery and
Acoustics Applications. [Doctoral Dissertation]. University of Cincinnati; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1543840344167045
27.
Fernanda Paula Barbosa.
Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem.
Degree: 2012, University of São Paulo
URL: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03042013-100331/
► A representação de malhas por meio de estrutura de dados e operadores topológicos e um dos focos principais da modelagem geométrica, onde permite uma implementação…
(more)
▼ A representação de malhas por meio de estrutura de dados e operadores topológicos e um dos focos principais da modelagem geométrica, onde permite uma implementação robusta e eficiente de mecanismos de refinamento adaptativo, alinhamento de células e acesso as relações de incidência e adjacência entre os elementos da malha, o que é de grande importância na maioria das aplicações em mecânica dos fluidos. No caso de malhas não estruturadas, a não uniformidade da decomposição celular e melhor representada por uma estrategia mais sofisticada, que são as estruturas de dados topológicas. As estruturas de dados topológicas indexam elementos de uma malha representando relações de incidência e adjacência entre elementos, garantindo acesso rápido às informações. Um dos aspectos mais comuns aos problemas tratados pela mecânica dos fluidos computacional é a complexidade da geometria do domínio onde ocorre o escoamento. O uso de estruturas de dados para
manipular malhas computacionais e de grande importância pois realiza de modo eficiente as consultas às informações da malha e centraliza todas as operações sobre a malha em um único módulo, possibilitando sua extensão e adaptação em diversas situações. Este trabalho visou explorar o acoplamento de uma estrutura de dados topológica, a Mate Face, em um módulo simulador existente, de modo a gerenciar todos os acessos à malha e dispor operações e iteradores para pesquisas complexas nas vizinhanças de cada elemento na malha. O módulo simulador resolve as equações governantes da mecânica dos fluidos através da técnica de volumes finitos. Foi utilizada uma formulação que atribui os valores das propriedades aos centroides dos volumes de controle, utiliza métodos de alta ordem, os esquemas ENO e WENO, que tem a finalidade de capturar com eficiência descontinuidades presentes em problemas governados por equações diferenciais parciais hiperbólicas. As equações de Euler em duas dimensões
representam os escoamentos de interesse no presente trabalho. O acoplamento da estrutura de dados Mate Face ao simulador foi realizada através da criação de uma biblioteca desenvolvida que atua como uma interface de comunicação entre os dois módulos, a estrutura de dados e o simulador, que foram implementados em diferentes linguagens de programação. Deste modo, todas as funcionalidades existentes na Mate Face tornaram-se acessíveis ao simulador na forma de procedimentos. Um estudo sobre malhas dinâmicas foi realizado envolvendo o método das molas para movimentação de malhas simulando-se operações de arfagem. A idéia foi verificar a aplicabilidade deste método para auxiliar simulações de escoamentos não estacionarios. Uma outra vertente do trabalho foi estender a estrutura Mate Face de forma a representar elementos não suportados a priori, de modo a flexibilizar o seu uso em simulações de escoamentos baseados no método de volumes finitos espectrais. O método dos volumes espectrais e
utilizado para se obter alta resolução espacial do domínio computacional, que também atribui valores das propriedades aos…
Advisors/Committee Members: Antonio Castelo Filho, Paulo Celso Greco Junior, Mario Augusto de Souza Liziér, Norberto Mangiavacchi, Leandro Franco de Souza.
Subjects/Keywords: Estrutura de dados; Volumes finitos e métodos de alta ordem; Data structures; Finite volume and high-order methods
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APA ·
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MLA ·
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APA (6th Edition):
Barbosa, F. P. (2012). Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03042013-100331/
Chicago Manual of Style (16th Edition):
Barbosa, Fernanda Paula. “Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem.” 2012. Doctoral Dissertation, University of São Paulo. Accessed April 16, 2021.
http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03042013-100331/.
MLA Handbook (7th Edition):
Barbosa, Fernanda Paula. “Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem.” 2012. Web. 16 Apr 2021.
Vancouver:
Barbosa FP. Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem. [Internet] [Doctoral dissertation]. University of São Paulo; 2012. [cited 2021 Apr 16].
Available from: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03042013-100331/.
Council of Science Editors:
Barbosa FP. Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem. [Doctoral Dissertation]. University of São Paulo; 2012. Available from: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-03042013-100331/
Uppsala University
28.
O'Reilly, Ossian.
Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries.
Degree: Information Technology, 2011, Uppsala University
URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471
► The linear elastodynamic two-dimensional anti-plane stress problem, where deformations occur in only one direction is considered for one sided non-planar faults. Fault dynamics are…
(more)
▼ The linear elastodynamic two-dimensional anti-plane stress problem, where deformations occur in only one direction is considered for one sided non-planar faults. Fault dynamics are modeled using purely velocity dependent friction laws, and applied on boundaries with complex geometry. Summation-by-parts operators and energy estimates are used to couple a high-order finite difference method with an unstructured finite volume method. The unstructured finite volume method is used near the fault and the high-order finite difference method further away from the fault where no complex geometry is present. Boundary conditions are imposed weakly on characteristic form using the simultaneous approximation term technique, allowing explicit time integration to be used. Numerical computations are performed to verify the accuracy and time stability, of the method.
Subjects/Keywords: SBP summation-by-parts SAT simultaneous-approximation-term unstructured finite volume methods high order finite difference methods interface coupling earthquake rupture dynamics complex geometries
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APA ·
Chicago ·
MLA ·
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CSE |
Export
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Manager
APA (6th Edition):
O'Reilly, O. (2011). Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
O'Reilly, Ossian. “Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries.” 2011. Thesis, Uppsala University. Accessed April 16, 2021.
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
O'Reilly, Ossian. “Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries.” 2011. Web. 16 Apr 2021.
Vancouver:
O'Reilly O. Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries. [Internet] [Thesis]. Uppsala University; 2011. [cited 2021 Apr 16].
Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
O'Reilly O. Coupled High-Order Finite Difference and Unstructured Finite Volume Methods for Earthquake Rupture Dynamics in Complex Geometries. [Thesis]. Uppsala University; 2011. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-155471
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
29.
Feuillet, Rémi.
Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite.
Degree: Docteur es, Mathématiques appliquées, 2019, Université Paris-Saclay (ComUE)
URL: http://www.theses.fr/2019SACLY010
► La simulation numérique de phénomènes physiques complexes requiert généralement l’utilisation d’un maillage. En mécanique des fluides numérique, cela consisteà représenter un objet dans un gros…
(more)
▼ La simulation numérique de phénomènes physiques complexes requiert généralement l’utilisation d’un maillage. En mécanique des fluides numérique, cela consisteà représenter un objet dans un gros volume de contrôle. Cet objet étant celui dont l’on souhaite simuler le comportement. Usuellement, l’objet et la boîte englobante sont représentés par des maillage de surface linéaires et la zone intermédiaire est remplie par un maillage volumique. L’objectif de cette thèse est de s’intéresser à deux manières différentes de représenter cet objet. La première approche dite immergée consiste à mailler intégralement le volume de contrôle et ensuite à simuler le comportement autour de l’objet sans avoir à mailler explicitement dans le volume ladite géometrie. L’objet étant implicitement pris en compte par le schéma numérique. Le couplage de cette méthode avec de l’adaptation de maillage linéaire est notamment étudié. La deuxième approche dite d’ordre élevé consiste quant à elle consiste à augmenter le degré polynomial du maillage de surface de l’objet. La première étape consiste donc à générer le maillage de surface de degré élevé et ensuite àpropager l’information de degré élevé dans les éléments volumiques environnants si nécessaire. Dans ce cadre-là, il s’agit de s’assurer de la validité de telles modifications et à considérer l’extension des méthodes classiques de modification de maillages linéaires.
The numerical simulation of complex physical phenomenons usually requires a mesh. In Computational Fluid Dynamics, it consists in representing an object inside a huge control volume. This object is then the subject of some physical study. In general, this object and its bounding box are represented by linear surface meshes and the intermediary zone is filled by a volume mesh. The aim of this thesis is to have a look on two different approaches for representing the object. The first approach called embedded method consist in integrally meshing the bounding box volume without explicitly meshing the object in it. In this case, the presence of the object is implicitly simulated by the CFD solver. The coupling of this method with linear mesh adaptation is in particular discussed.The second approach called high-order method consist on the contrary by increasing the polynomial order of the surface mesh of the object. The first step is therefore to generate a suitable high-order mesh and then to propagate the high-order information in the neighboring volume if necessary. In this context, it is mandatory to make sure that such modifications are valid and then the extension of classic mesh modification techniques has to be considered.
Advisors/Committee Members: Ciarlet, Patrick (thesis director), Alauzet, Frédéric (thesis director).
Subjects/Keywords: Méthodes d'ordre élevé; Visualisation scientifique; Méthodes immergées; Mécanique des fluides numérique; Adaptation de maillage; High-Order methods; Scientific visualization; Embedded methods; Cfd; Mesh adaptation
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APA ·
Chicago ·
MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Feuillet, R. (2019). Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite. (Doctoral Dissertation). Université Paris-Saclay (ComUE). Retrieved from http://www.theses.fr/2019SACLY010
Chicago Manual of Style (16th Edition):
Feuillet, Rémi. “Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite.” 2019. Doctoral Dissertation, Université Paris-Saclay (ComUE). Accessed April 16, 2021.
http://www.theses.fr/2019SACLY010.
MLA Handbook (7th Edition):
Feuillet, Rémi. “Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite.” 2019. Web. 16 Apr 2021.
Vancouver:
Feuillet R. Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite. [Internet] [Doctoral dissertation]. Université Paris-Saclay (ComUE); 2019. [cited 2021 Apr 16].
Available from: http://www.theses.fr/2019SACLY010.
Council of Science Editors:
Feuillet R. Embedded and high-order meshes : two alternatives to linear body-fitted meshes : Maillages immergés et d'ordre élevé : deux alternatives à la représentation linéaire des maillages en géométrie inscrite. [Doctoral Dissertation]. Université Paris-Saclay (ComUE); 2019. Available from: http://www.theses.fr/2019SACLY010
University of Notre Dame
30.
Tian Jiang.
Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>.
Degree: Applied and Computational Mathematics and
Statistics, 2015, University of Notre Dame
URL: https://curate.nd.edu/show/xs55m90370p
► There are two parts of my thesis. The first part is about muilti-step Krylov IIF-WENO methods. When we are dealing with time-dependent partial differential…
(more)
▼ There are two parts of my thesis. The first
part is about muilti-step Krylov IIF-WENO
methods. When we are
dealing with time-dependent partial differential equations (PDEs)
with linear
high order terms and stiff lower
order nonlinear terms,
implicit integration factor (IIF)
methods are often a good choice
as a class of efficient “exactly linear part” time discretization
method. In complex systems (e.g. advection-diffusion-reaction (ADR)
systems), the highest
order derivative term can be nonlinear, and
nonlinear non-stiff terms and nonlinear stiff terms are often mixed
together. To discretize the hyperbolic part in ADR systems,
high
order weighted essentially non-oscillatory (WENO)
methods are often
used. There are two open problems related to IIF
methods for
solving ADR systems: (1) how to obtain higher than the second
order
global time discretization accuracy; (2) how to design IIF
methods
for solving fully nonlinear PDEs, i.e., the highest
order terms are
nonlinear. We solve these two problems by developing new
muilti-step Krylov IIF-WENO
methods to deal with both semilinear
and fully nonlinear advection-diffusion-reaction equations. The
methods can be designed for arbitrary
order of accuracy. The
stiffness of the system is resolved well and the
methods are stable
by using time step sizes which are just determined by the non-stiff
hyperbolic part of the system. Large time step size computations
are obtained. The second part is about
single-step Krylov IIF-WENO
methods. So far, the IIF
methods
developed in the literature are multi-step
methods. Hence, we
develop single-step Krylov IIF-WENO
methods for solving stiff
advection-diffusion-reaction equations. The
methods are designed
carefully to avoid generating positive exponentials in the matrix
exponentials, which is necessary for the stability of the schemes.
We analyze the stability and truncation errors of both the
single-step and multi-step schemes. Numerical examples of both
scalar equations and systems are shown to demonstrate the accuracy,
efficiency and robustness of these two
schemes.
Advisors/Committee Members: Andrew Sommese, Committee Member, Bei Hu, Committee Member, Robert Rosenbaum, Committee Member, Yongtao Zhang, Committee Chair.
Subjects/Keywords: Weighted essentially non-oscillatory schemes.; Single-step methods; High order accuracy; Advection-diffusion-reaction equations; Implicit integration factor methods; Krylov subspace approximation
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Jiang, T. (2015). Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>. (Thesis). University of Notre Dame. Retrieved from https://curate.nd.edu/show/xs55m90370p
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Jiang, Tian. “Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>.” 2015. Thesis, University of Notre Dame. Accessed April 16, 2021.
https://curate.nd.edu/show/xs55m90370p.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Jiang, Tian. “Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>.” 2015. Web. 16 Apr 2021.
Vancouver:
Jiang T. Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>. [Internet] [Thesis]. University of Notre Dame; 2015. [cited 2021 Apr 16].
Available from: https://curate.nd.edu/show/xs55m90370p.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Jiang T. Krylov Implicit Integration Factor WENO Methods for Stiff
Advection-Diffusion-Reaction Equations</h1>. [Thesis]. University of Notre Dame; 2015. Available from: https://curate.nd.edu/show/xs55m90370p
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
◁ [1] [2] [3] ▶
. 
Open Access Theses and Dissertations
