You searched for +publisher:"Virginia Tech" +contributor:("Iliescu, Traian").
Showing records 1 – 30 of
34 total matches.
◁ [1] [2] ▶
No search limiters apply to these results.
Virginia Tech
1.
Xie, Xuping.
Approximate Deconvolution Reduced Order Modeling.
Degree: MS, Mathematics, 2015, Virginia Tech
URL: http://hdl.handle.net/10919/78043 
► This thesis proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper…
(more)
▼ This thesis proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient ( ν= 10⁻³).
Advisors/Committee Members: Iliescu, Traian (committeechair), Gugercin, Serkan (committee member), Lin, Tao (committee member).
Subjects/Keywords: approximate deconvolution; large eddy simulation; reduced order modeling; inverse problems; regularization
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Xie, X. (2015). Approximate Deconvolution Reduced Order Modeling. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/78043
Chicago Manual of Style (16th Edition):
Xie, Xuping. “Approximate Deconvolution Reduced Order Modeling.” 2015. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/78043.
MLA Handbook (7th Edition):
Xie, Xuping. “Approximate Deconvolution Reduced Order Modeling.” 2015. Web. 13 Apr 2021.
Vancouver:
Xie X. Approximate Deconvolution Reduced Order Modeling. [Internet] [Masters thesis]. Virginia Tech; 2015. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/78043.
Council of Science Editors:
Xie X. Approximate Deconvolution Reduced Order Modeling. [Masters Thesis]. Virginia Tech; 2015. Available from: http://hdl.handle.net/10919/78043
Virginia Tech
2.
Wells, David Reese.
A Two-Level Method For The Steady-State Quasigeostrophic Equation.
Degree: MS, Mathematics, 2013, Virginia Tech
URL: http://hdl.handle.net/10919/23090
► The quasi-geostrophic equations (QGE) are a model of large-scale ocean flows. We consider a pure stream function formulation and cite results for optimal error estimates…
(more)
▼ The quasi-geostrophic equations (QGE) are a model of large-scale ocean flows. We consider a pure stream function formulation and cite results for optimal error estimates for finding approximate solutions with the finite element method. We examine both the time dependent and steady-state versions of the equations. Numerical experiments verify the error estimates. We examine the Argyris finite element and derive the transformation matrix necessary to perform calculations on the reference triangle. We use the Argyris element because it is a high-order, conforming finite element for fourth order problems. In order to increase computational efficiency, we consider a two-level method to linearize the system of equations. This allows us to solve a small, nonlinear system and then use the result to linearize a larger system.
Advisors/Committee Members: Iliescu, Traian (committeechair), Lin, Tao (committee member), Adjerid, Slimane (committee member).
Subjects/Keywords: Quasi-geostrophic equations; Finite Element Method; Argyris Element; Two-Level Method
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wells, D. R. (2013). A Two-Level Method For The Steady-State Quasigeostrophic Equation. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/23090
Chicago Manual of Style (16th Edition):
Wells, David Reese. “A Two-Level Method For The Steady-State Quasigeostrophic Equation.” 2013. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/23090.
MLA Handbook (7th Edition):
Wells, David Reese. “A Two-Level Method For The Steady-State Quasigeostrophic Equation.” 2013. Web. 13 Apr 2021.
Vancouver:
Wells DR. A Two-Level Method For The Steady-State Quasigeostrophic Equation. [Internet] [Masters thesis]. Virginia Tech; 2013. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/23090.
Council of Science Editors:
Wells DR. A Two-Level Method For The Steady-State Quasigeostrophic Equation. [Masters Thesis]. Virginia Tech; 2013. Available from: http://hdl.handle.net/10919/23090
Virginia Tech
3.
Koc, Birgul.
Commutation Error in Reduced Order Modeling.
Degree: MS, Mathematics, 2018, Virginia Tech
URL: http://hdl.handle.net/10919/87537
► We propose reduced order models (ROMs) for an efficient and relatively accurate numerical simulation of nonlinear systems. We use the ROM projection and the ROM…
(more)
▼ We propose reduced order models (ROMs) for an efficient and relatively accurate numerical simulation of nonlinear systems. We use the ROM projection and the ROM differential filters to construct a novel data-driven correction ROM (DDC-ROM). We show that the ROM spatial filtering and differentiation do not commute for the diffusion operator. Furthermore, we show that the resulting commutation error has an important effect on the ROM, especially for low viscosity values. As a mathematical model for our numerical study, we use the one-dimensional Burgers equations with smooth and non-smooth initial conditions.
Advisors/Committee Members: Iliescu, Traian (committeechair), Borggaard, Jeffrey T. (committee member), Gugercin, Serkan (committee member).
Subjects/Keywords: Reduced Order Modeling; Data-Driven Modeling; Filtering; Closure Modeling; Commutation Error
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Koc, B. (2018). Commutation Error in Reduced Order Modeling. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/87537
Chicago Manual of Style (16th Edition):
Koc, Birgul. “Commutation Error in Reduced Order Modeling.” 2018. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/87537.
MLA Handbook (7th Edition):
Koc, Birgul. “Commutation Error in Reduced Order Modeling.” 2018. Web. 13 Apr 2021.
Vancouver:
Koc B. Commutation Error in Reduced Order Modeling. [Internet] [Masters thesis]. Virginia Tech; 2018. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/87537.
Council of Science Editors:
Koc B. Commutation Error in Reduced Order Modeling. [Masters Thesis]. Virginia Tech; 2018. Available from: http://hdl.handle.net/10919/87537
4.
Mou, Changhong.
Cross-Validation of Data-Driven Correction Reduced Order Modeling.
Degree: MS, Mathematics, 2018, Virginia Tech
URL: http://hdl.handle.net/10919/87610
► Practical engineering and scientific problems often require the repeated simulation of unsteady fluid flows. In these applications, the computational cost of high-fidelity full-order models can…
(more)
▼ Practical engineering and scientific problems often require the repeated simulation of unsteady fluid flows. In these applications, the computational cost of high-fidelity full-order models can be prohibitively high. Reduced order models (ROMs) represent efficient alternatives to brute force computational approaches. In this thesis, we propose a data-driven correction ROM (DDC-ROM) in which available data and an optimization problem are used to model the nonlinear interactions between resolved and unresolved modes. In order to test the new DDC-ROM's predictability, we perform its cross-validation for the one-dimensional viscous Burgers equation and different training regimes.
Advisors/Committee Members: Iliescu, Traian (committeechair), Burns, John A. (committee member), Liu, Honghu (committee member).
Subjects/Keywords: Reduced Order Modeling; Scientific Computing; Data-Driven Modeling; Optimization
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mou, C. (2018). Cross-Validation of Data-Driven Correction Reduced Order Modeling. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/87610
Chicago Manual of Style (16th Edition):
Mou, Changhong. “Cross-Validation of Data-Driven Correction Reduced Order Modeling.” 2018. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/87610.
MLA Handbook (7th Edition):
Mou, Changhong. “Cross-Validation of Data-Driven Correction Reduced Order Modeling.” 2018. Web. 13 Apr 2021.
Vancouver:
Mou C. Cross-Validation of Data-Driven Correction Reduced Order Modeling. [Internet] [Masters thesis]. Virginia Tech; 2018. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/87610.
Council of Science Editors:
Mou C. Cross-Validation of Data-Driven Correction Reduced Order Modeling. [Masters Thesis]. Virginia Tech; 2018. Available from: http://hdl.handle.net/10919/87610
5.
Norton, Trevor Michael.
Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays.
Degree: MS, Mathematics, 2018, Virginia Tech
URL: http://hdl.handle.net/10919/83825
► Delay differential equations (DDEs) are often used to model systems with time-delayed effects, and they have found applications in fields such as climate dynamics, biosciences,…
(more)
▼ Delay differential equations (DDEs) are often used to model systems with time-delayed effects, and they have found applications in fields such as climate dynamics, biosciences, engineering, and control theory. In contrast to ordinary differential equations (ODEs), the phase space associated even with a scalar DDE is infinite-dimensional. Oftentimes, it is desirable to have low-dimensional ODE systems that capture qualitative features as well as approximate certain quantitative aspects of the DDE dynamics. In this thesis, we present a Galerkin scheme for a broad class of DDEs and derive convergence results for this scheme. In contrast to other Galerkin schemes devised in the DDE literature, the main new ingredient here is the use of the so called Koornwinder polynomials, which are orthogonal polynomials under an inner product with a point mass. A main advantage of using such polynomials is that they live in the domain of the underlying linear operator, which arguably simplifies the related numerical treatments. The obtained results generalize a previous work to the case of DDEs with multiply delays in the linear terms, either discrete or distributed, or both. We also consider the more challenging case of discrete delays in the nonlinearity and obtain a convergence result by assuming additional assumptions about the Galerkin approximations of the linearized systems.
Advisors/Committee Members: Liu, Honghu (committeechair), Sun, Shu Ming (committee member), Iliescu, Traian (committee member).
Subjects/Keywords: Delay Differential Equations; Galerkin Approximations
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Norton, T. M. (2018). Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/83825
Chicago Manual of Style (16th Edition):
Norton, Trevor Michael. “Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays.” 2018. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/83825.
MLA Handbook (7th Edition):
Norton, Trevor Michael. “Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays.” 2018. Web. 13 Apr 2021.
Vancouver:
Norton TM. Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays. [Internet] [Masters thesis]. Virginia Tech; 2018. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/83825.
Council of Science Editors:
Norton TM. Galerkin Approximations of General Delay Differential Equations with Multiple Discrete or Distributed Delays. [Masters Thesis]. Virginia Tech; 2018. Available from: http://hdl.handle.net/10919/83825
6.
Letona Bolivar, Cristina Felicitas.
On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.
Degree: PhD, Mathematics, 2016, Virginia Tech
URL: http://hdl.handle.net/10919/73308
► The methods for solving domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but…
(more)
▼ The methods for solving domain optimization problems depends on the case of study. There are methods that have been developed for the discretized problem, but not much is done in the infinite dimensional case. We analyze the theoretical aspects of the infinite dimensional case for a particular domain optimization problem where a portion of the boundary is parametrized, these results involve the existence of the solution to our problem and the calculation of the derivative of the shape functional.
Shape optimization problems have a long history of mathematical study and a wide range of applications. In recent decades there has been an interest in solving these problems with partial differential equation (PDE) constraints. We consider a special class of PDE-constrained shape optimization problems where different boundary condition types (Dirichlet and Neumann) are imposed on the same boundary segment. We also consider the case where the interface between these different boundary condition types may also be parameter dependent. This study also includes special cases where the shape of the region where the PDE is imposed does not change, but the domain of the partial differential operator is parameter dependent, due to the change in boundary condition type. Our treatment centers on the infinite dimensional formulation of the optimization problem. We consider existence of solutions as well as the calculation of derivatives of the associated shape functionals via adjoint solutions. These derivative formulations serve as a starting point for practical numerical approximations.
Advisors/Committee Members: Borggaard, Jeffrey T. (committeechair), Zietsman, Lizette (committee member), Iliescu, Traian (committee member), Lin, Tao (committee member).
Subjects/Keywords: Domain Optimization; Shape Derivatives; PDE Constraints; Mixed Boundary Conditions.
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Letona Bolivar, C. F. (2016). On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/73308
Chicago Manual of Style (16th Edition):
Letona Bolivar, Cristina Felicitas. “On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.” 2016. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/73308.
MLA Handbook (7th Edition):
Letona Bolivar, Cristina Felicitas. “On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types.” 2016. Web. 13 Apr 2021.
Vancouver:
Letona Bolivar CF. On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. [Internet] [Doctoral dissertation]. Virginia Tech; 2016. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/73308.
Council of Science Editors:
Letona Bolivar CF. On a Class of Parametrized Domain Optimization Problems with Mixed Boundary Condition Types. [Doctoral Dissertation]. Virginia Tech; 2016. Available from: http://hdl.handle.net/10919/73308
Virginia Tech
7.
Xie, Xuping.
Large Eddy Simulation Reduced Order Models.
Degree: PhD, Mathematics, 2017, Virginia Tech
URL: http://hdl.handle.net/10919/77626
► This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to…
(more)
▼ This dissertation uses spatial filtering to develop a large eddy simulation reduced order model (LES-ROM) framework for fluid flows. Proper orthogonal decomposition is utilized to extract the dominant spatial structures of the system. Within the general LES-ROM framework, two approaches are proposed to address the celebrated ROM closure problem. No phenomenological arguments (e.g., of eddy viscosity type) are used to develop these new ROM closure models.
The first novel model is the approximate deconvolution ROM (AD-ROM), which uses methods from image processing and inverse problems to solve the ROM closure problem. The AD-ROM is investigated in the numerical simulation of a 3D flow past a circular cylinder at a Reynolds number Re=1000. The AD-ROM generates accurate results without any numerical dissipation mechanism. It also decreases the CPU time of the standard ROM by orders of magnitude.
The second new model is the calibrated-filtered ROM (CF-ROM), which is a data-driven ROM. The available full order model results are used offline in an optimization problem to calibrate the ROM subfilter-scale stress tensor. The resulting CF-ROM is tested numerically in the simulation of the 1D Burgers equation with a small diffusion parameter. The numerical results show that the CF-ROM is more efficient than and as accurate as state-of-the-art ROM closure models.
Advisors/Committee Members: Iliescu, Traian (committeechair), Borggaard, Jeffrey T. (committee member), Gugercin, Serkan (committee member), Ross, Shane D. (committee member).
Subjects/Keywords: Reduced Order Modeling; Large Eddy Simulation; Approximate Deconvolution; Data-Driven Modeling; Stochastic Reduced Order Model; Spatial Filtering; Finite Element; Numerical Analysis
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Xie, X. (2017). Large Eddy Simulation Reduced Order Models. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/77626
Chicago Manual of Style (16th Edition):
Xie, Xuping. “Large Eddy Simulation Reduced Order Models.” 2017. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/77626.
MLA Handbook (7th Edition):
Xie, Xuping. “Large Eddy Simulation Reduced Order Models.” 2017. Web. 13 Apr 2021.
Vancouver:
Xie X. Large Eddy Simulation Reduced Order Models. [Internet] [Doctoral dissertation]. Virginia Tech; 2017. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/77626.
Council of Science Editors:
Xie X. Large Eddy Simulation Reduced Order Models. [Doctoral Dissertation]. Virginia Tech; 2017. Available from: http://hdl.handle.net/10919/77626
Virginia Tech
8.
Basu, Saikat.
Dynamics of vortices in complex wakes: modeling, analysis, and experiments.
Degree: PhD, Engineering Mechanics, 2014, Virginia Tech
URL: http://hdl.handle.net/10919/51749
► The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns…
(more)
▼ The thesis develops singly-periodic mathematical models for complex laminar wakes which are formed behind vortex-shedding bluff bodies. These wake structures exhibit a variety of patterns as the bodies oscillate or are in close proximity of one another. The most well-known formation comprises two counter-rotating vortices in each shedding cycle and is popularly known as the vk vortex street. Of the more complex configurations, as a specific example, this thesis investigates one of the most commonly occurring wake arrangements, which consists of two pairs of vortices in each shedding period. The paired vortices are, in general, counter-rotating and belong to a more general definition of the 2P mode, which involves periodic release of four vortices into the flow. The 2P arrangement can, primarily, be sub-classed into two types: one with a symmetric orientation of the two vortex pairs about the streamwise direction in a periodic domain and the other in which the two vortex pairs per period are placed in a staggered geometry about the wake centerline. The thesis explores the governing dynamics of such wakes and characterizes the corresponding relative vortex motion.
In general, for both the symmetric as well as the staggered four vortex periodic arrangements, the thesis develops two-dimensional potential flow models (consisting of an integrable Hamiltonian system of point vortices) that consider spatially periodic arrays of four vortices with their strengths being +/-1 and +/-2. Vortex formations observed in the experiments inspire the assumed spatial symmetry. The models demonstrate a number of dynamic modes that are classified using a bifurcation analysis of the phase space topology, consisting of level curves of the Hamiltonian. Despite the vortex strengths in each pair being unequal in magnitude, some initial conditions lead to relative equilibrium when the vortex configuration moves with invariant size and shape.
The scaled comparisons of the model results with experiments conducted in a flowing soap film with an airfoil, which was imparted with forced oscillations, are satisfactory and validate the reduced order modeling framework. The experiments have been performed by a collaborator group at the Department of Physics and Fluid Dynamics at the Technical University of Denmark (DTU), led by Dr. Anders Andersen. Similar experiments have also been run at
Virginia Tech as part of this dissertation and the preliminary results are included in this treatise.
The thesis also employs the same dynamical systems techniques, which have been applied to study the 2P regime dynamics, to develop a mathematical model for the P+S mode vortex wakes, with three vortices present in each shedding cycle. The model results have also been compared favorably with an experiment and the predictions regarding the vortex circulation data match well with the previous results from literature.
Finally, the thesis introduces a novel concept of clean and renewable energy extraction from vortex-induced vibrations of bluff bodies. The slow-moving…
Advisors/Committee Members: Stremler, Mark A. (committeechair), Jung, Sunghwan (committee member), Iliescu, Traian (committee member), Ross, Shane D. (committee member), Ragab, Saad A. (committee member).
Subjects/Keywords: Vortex dynamics; Point vortices; Bluff body wake; Fluid-structure interactions; Vortex-induced vibrations
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Basu, S. (2014). Dynamics of vortices in complex wakes: modeling, analysis, and experiments. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/51749
Chicago Manual of Style (16th Edition):
Basu, Saikat. “Dynamics of vortices in complex wakes: modeling, analysis, and experiments.” 2014. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/51749.
MLA Handbook (7th Edition):
Basu, Saikat. “Dynamics of vortices in complex wakes: modeling, analysis, and experiments.” 2014. Web. 13 Apr 2021.
Vancouver:
Basu S. Dynamics of vortices in complex wakes: modeling, analysis, and experiments. [Internet] [Doctoral dissertation]. Virginia Tech; 2014. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/51749.
Council of Science Editors:
Basu S. Dynamics of vortices in complex wakes: modeling, analysis, and experiments. [Doctoral Dissertation]. Virginia Tech; 2014. Available from: http://hdl.handle.net/10919/51749
Virginia Tech
9.
Bozorg Magham, Amir Ebrahim.
Atmospheric Lagrangian transport structures and their applications to aerobiology.
Degree: PhD, Engineering Mechanics, 2014, Virginia Tech
URL: http://hdl.handle.net/10919/56482
► Exploring the concepts of long range aerial transport of microorganisms is the main motivation of this study. For this purpose we use theories and concepts…
(more)
▼ Exploring the concepts of long range aerial transport of microorganisms is the main motivation of this study. For this purpose we use theories and concepts of dynamical systems in the context of geophysical fluid systems. We apply powerful notions such as finite-time Lyapunov exponent (FTLE) and the associated Lagrangian coherent structures (LCS) and we attempt to provide mathematical explanations and frameworks for some applied questions which are based on realistic concerns of atmospheric transport phenomena. Accordingly, we quantify the accuracy of prediction of FTLE-LCS features and we determine the sensitivity of such predictions to forecasting parameters. In addition, we consider the spatiotemporal resolution of the operational data sets and we propose the concept of probabilistic source and destination regions which leads to the definition of stochastic FTLE fields. Moreover, we put forward the idea of using ensemble forecasting to quantify the uncertainty of the forecast results. Finally, we investigate the statistical properties of localized measurements of atmospheric microbial structure and their connections to the concept of local FTLE time-series.
Results of this study would pave the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans.
Advisors/Committee Members: Ross, Shane D. (committeechair), Schmale, David G. III (committeechair), Iliescu, Traian (committee member), Stremler, Mark A. (committee member), Paul, Mark R. (committee member).
Subjects/Keywords: Finite-time Lyapunov exponent (FTLE); Lagrangian coherent structure (LCS); chaotic atmospheric transport; unresolved turbulence; stochastic FTLE field; ensemble forecasting; uncertainty analysis; local FTLE time-series; maximal diversity monitoring
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Bozorg Magham, A. E. (2014). Atmospheric Lagrangian transport structures and their applications to aerobiology. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/56482
Chicago Manual of Style (16th Edition):
Bozorg Magham, Amir Ebrahim. “Atmospheric Lagrangian transport structures and their applications to aerobiology.” 2014. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/56482.
MLA Handbook (7th Edition):
Bozorg Magham, Amir Ebrahim. “Atmospheric Lagrangian transport structures and their applications to aerobiology.” 2014. Web. 13 Apr 2021.
Vancouver:
Bozorg Magham AE. Atmospheric Lagrangian transport structures and their applications to aerobiology. [Internet] [Doctoral dissertation]. Virginia Tech; 2014. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/56482.
Council of Science Editors:
Bozorg Magham AE. Atmospheric Lagrangian transport structures and their applications to aerobiology. [Doctoral Dissertation]. Virginia Tech; 2014. Available from: http://hdl.handle.net/10919/56482
Virginia Tech
10.
Nolan, Peter Joseph.
Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport.
Degree: PhD, Engineering Mechanics, 2019, Virginia Tech
URL: http://hdl.handle.net/10919/88986
► How particles are moved by fluid flows, such as the oceanic currents and the atmospheric winds, is a problem with important implications for fields as…
(more)
▼ How particles are moved by fluid flows, such as the oceanic currents and the atmospheric winds, is a problem with important implications for fields as diverse as: agriculture, aviation, human health, disaster response, and weather forecasting. Because these fluid flows tend to change over time, predicting how particles will be moved by these flows can often be challenging. Fortunately, mathematical tools exist which can reveal important geometric features in these flows. These geometric features can help us to visualize regions where particles are likely to come together or spread apart, as they are moved by the flow. In the past, these geometric features have been uncovered by using methods which look at the trajectories of particles in the flow. These methods are referred to as Lagrangian, in honor of the Italian mathematician Joseph-Louis Lagrange. Unfortunately, calculating the trajectories of particles can be a time consuming and computationally expensive process. Recently, new methods have been developed which look at how the speed of the flow changes in space. These new methods are referred to as Eulerian, in honor of the Swiss mathematician Leonhard Euler. These new Eulerian methods are faster and less expensive to calculate, while still revealing important geometric features within the flow. Because these Eulerian methods are so new, there is still much that we do not know about them and their connection to the older Lagrangian methods. This dissertation will fill in some of this gap and provide a mathematical bridge between these two methodologies. This dissertation is composed of three projects. These projects represent theoretical, numerical, and experimental advances in the understanding of these new Eulerian methods and their relationship to the older Lagrangian methods. The first project explores the deep mathematical relationship that exists between Eulerian and Lagrangian diagnostic tools. It mathematically proves that some of the new Eulerian diagnostics are the limit of Lagrangian diagnostics as the trajectory’s integration times is decreased to zero. Taking advantage of this discovery, a new Eulerian diagnostic is developed, called infinitesimal-time Lagrangian coherent structures. The second project develops a technique for estimating local Eulerian diagnostics using wind speed measures from a single fixed-wing unmanned aircraft system (UAS) flying in a circular path. Using computer simulations, we show that the Eulerian diagnostics as calculated from UAS measurements provide a reasonable estimate of the true local Eulerian diagnostics. Furthermore, we show that these Eulerian diagnostics can be used to estimate the local Lagrangian diagnostics. The third project applies these Eulerian diagnostics to real-world wind speed measurements. These results are then compared to Eulerian diagnostics that were calculated from a computer simulation to look for indications of Lagrangian diagnostics.
Advisors/Committee Members: Ross, Shane D. (committeechair), Schmale, David G. III (committee member), Iliescu, Traian (committee member), Foroutan, Hosein (committee member), Woolsey, Craig A. (committee member).
Subjects/Keywords: Lagrangian coherent structures; geophysical fluid mechanics; dynamical systems
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Nolan, P. J. (2019). Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/88986
Chicago Manual of Style (16th Edition):
Nolan, Peter Joseph. “Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport.” 2019. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/88986.
MLA Handbook (7th Edition):
Nolan, Peter Joseph. “Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport.” 2019. Web. 13 Apr 2021.
Vancouver:
Nolan PJ. Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport. [Internet] [Doctoral dissertation]. Virginia Tech; 2019. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/88986.
Council of Science Editors:
Nolan PJ. Experimental and Theoretical Developments in the Application of Lagrangian Coherent Structures to Geophysical Transport. [Doctoral Dissertation]. Virginia Tech; 2019. Available from: http://hdl.handle.net/10919/88986
Virginia Tech
11.
Jin, Hanxiang.
Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery.
Degree: PhD, Engineering Mechanics, 2020, Virginia Tech
URL: http://hdl.handle.net/10919/96731
► This dissertation focused on understanding the correlations between surface patterning and rotordynamic responses in the annular pressure seals. The annular pressure seals are a specific…
(more)
▼ This dissertation focused on understanding the correlations between surface patterning and rotordynamic responses in the annular pressure seals. The annular pressure seals are a specific type of rotordynamic component that was designed to prevent the fluid leakage from high pressure stage to low pressure stage in turbomachinery. As the working fluid enters the cavities and recirculates, the kinetic energy is reduced, resulting in a reduction of leakage flow through the annular pressure seals. Rotordynamic instability becomes an issue that may be related to the annular pressure seals in some cases. In recent years, rotordynamic components with higher rotor speeds and higher power densities are commonly used in industrial applications. These features could lead to increased instability risk in rotor-bearing systems as fluids-structure interactions take place. Therefore, high precision modeling of the rotodynamic components is required to predict the instability issues in high performance rotordynamic design. The instability issue may potentially be eliminated in design stage by varying the characteristics of the potentially unstable components. In this study, the surface patterning and rotordynamic responses were investigated for several different annular pressure seal models with a hybrid Bulk Flow/Computational Fluid Dynamics method. This dissertation provides for the first time regression models for rotordynamic coefficients that can be used as optimization guidelines. Research topics related to the annular pressure seals were presented in this dissertation as well. The reduced order model of both hole-pattern seals and labyrinth seals were investigated. The results showed that the flow field representing the flow dynamics in annular pressure seals can be expressed as a combination of first three proper orthogonal decomposition modes. In addition, supercritical state of carbon dioxide (sCO2) process fluid was examined to better understand the effects of working fluid on annular pressure seals. The results showed that the performance and stability in the annular pressure seals using sCO2 as process fluid can both be improved.
Advisors/Committee Members: Untaroiu, Alexandrina (committeechair), Staples, Anne E. (committee member), Iliescu, Traian (committee member), Boreyko, Jonathan B. (committee member), Untaroiu, Costin D. (committee member).
Subjects/Keywords: Fluid Dynamics; Annular Pressure Seals; Rotordynamics; Labyrinth Seals; Hole-pattern Seals; Reduced Order Modeling
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Jin, H. (2020). Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/96731
Chicago Manual of Style (16th Edition):
Jin, Hanxiang. “Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery.” 2020. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/96731.
MLA Handbook (7th Edition):
Jin, Hanxiang. “Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery.” 2020. Web. 13 Apr 2021.
Vancouver:
Jin H. Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery. [Internet] [Doctoral dissertation]. Virginia Tech; 2020. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/96731.
Council of Science Editors:
Jin H. Surface Patterning and Rotordynamic Response of Annular Pressure Seals Used in Turbomachinery. [Doctoral Dissertation]. Virginia Tech; 2020. Available from: http://hdl.handle.net/10919/96731
Virginia Tech
12.
Cioaca, Alexandru George.
A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation.
Degree: PhD, Computer Science and Applications, 2013, Virginia Tech
URL: http://hdl.handle.net/10919/51795
► A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data…
(more)
▼ A deep scientific understanding of complex physical systems, such as the atmosphere, can be achieved neither by direct measurements nor by numerical simulations alone. Data assimilation is a rigorous procedure to fuse information from a priori knowledge of the system state, the physical laws governing the evolution of the system, and real measurements, all with associated error statistics. Data assimilation produces best (a posteriori) estimates of model states and parameter values, and results in considerably improved
computer simulations.
The acquisition and use of observations in data assimilation raises several important scientific questions related to optimal sensor network design, quantification of data impact, pruning redundant data, and identifying the most beneficial additional observations. These questions originate in operational data assimilation practice, and have started to attract considerable interest in the recent past.
This dissertation advances the state of knowledge in four dimensional variational (4D-Var) - data assimilation by developing, implementing, and validating a novel computational framework for estimating observation impact and for optimizing sensor networks. The framework builds on the powerful methodologies of second-order adjoint modeling and the 4D-Var sensitivity equations. Efficient computational approaches for quantifying the observation impact include matrix free linear algebra algorithms and low-rank approximations of the sensitivities to observations. The sensor network configuration problem is formulated as a meta-optimization problem. Best values for parameters such as sensor location are obtained by optimizing a performance criterion, subject to the constraint posed by the 4D-Var optimization. Tractable computational solutions to this "optimization-constrained" optimization problem are provided.
The results of this work can be directly applied to the deployment of intelligent sensors and adaptive observations, as well as to reducing the operating costs of measuring networks, while preserving their ability to capture the essential features of the system under consideration.
Advisors/Committee Members: Sandu, Adrian (committeechair), Shaffer, Clifford A. (committee member), Ribbens, Calvin J. (committee member), De Sturler, Eric (committee member), Iliescu, Traian (committee member).
Subjects/Keywords: data assimilation; dynamic data-driven problem; second-order adjoints; adaptive observations; sensor placement; intelligent sensors; sensitivity analysis; uncertainty quantification; nonlinear optimization; inverse problems; parameter estimation; matrix-free linear solvers; truncated singular value decomposition
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Cioaca, A. G. (2013). A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/51795
Chicago Manual of Style (16th Edition):
Cioaca, Alexandru George. “A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation.” 2013. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/51795.
MLA Handbook (7th Edition):
Cioaca, Alexandru George. “A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation.” 2013. Web. 13 Apr 2021.
Vancouver:
Cioaca AG. A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation. [Internet] [Doctoral dissertation]. Virginia Tech; 2013. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/51795.
Council of Science Editors:
Cioaca AG. A Computational Framework for Assessing and Optimizing the Performance of Observational Networks in 4D-Var Data Assimilation. [Doctoral Dissertation]. Virginia Tech; 2013. Available from: http://hdl.handle.net/10919/51795
Virginia Tech
13.
Carracedo Rodriguez, Andrea.
Approximation of Parametric Dynamical Systems.
Degree: PhD, Mathematics, 2020, Virginia Tech
URL: http://hdl.handle.net/10919/99895
► Simulation of mathematical models plays an important role in the development of science. There is a wide range of models and approaches that depend on…
(more)
▼ Simulation of mathematical models plays an important role in the development of science.
There is a wide range of models and approaches that depend on the information available
and the goal of the problem. In this dissertation we focus on three problems whose solution
depends on parameters and for which we have either data resulting from simulations of the
model or a explicit structure that describes the model. First, for the case when only data are
available, we develop an algorithm that builds a data-driven approximation that is then easy
to reevaluate. Second, we embed our algorithm in an already developed framework for the
solution of a specific kind of model structure: nonlinear eigenvalue problems. Third, given
a model with a specific nonlinear structure, we develop a method to build a model with the
same structure, smaller dimension (for faster computation), and that provides an accurate
approximation of the original model.
Advisors/Committee Members: Gugercin, Serkan (committeechair), Iliescu, Traian (committee member), Borggaard, Jeffrey T. (committee member), Embree, Mark Partick (committee member), Beattie, Christopher A. (committee member).
Subjects/Keywords: Rational Approximation; Bilinear Model Reduction; Barycentric; Interpolation
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Carracedo Rodriguez, A. (2020). Approximation of Parametric Dynamical Systems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/99895
Chicago Manual of Style (16th Edition):
Carracedo Rodriguez, Andrea. “Approximation of Parametric Dynamical Systems.” 2020. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/99895.
MLA Handbook (7th Edition):
Carracedo Rodriguez, Andrea. “Approximation of Parametric Dynamical Systems.” 2020. Web. 13 Apr 2021.
Vancouver:
Carracedo Rodriguez A. Approximation of Parametric Dynamical Systems. [Internet] [Doctoral dissertation]. Virginia Tech; 2020. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/99895.
Council of Science Editors:
Carracedo Rodriguez A. Approximation of Parametric Dynamical Systems. [Doctoral Dissertation]. Virginia Tech; 2020. Available from: http://hdl.handle.net/10919/99895
Virginia Tech
14.
Karimi, Alireza.
Gaining New Insights into Spatiotemporal Chaos with Numerics.
Degree: PhD, Engineering Science and Mechanics, 2012, Virginia Tech
URL: http://hdl.handle.net/10919/77347
► An important phenomenon of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for…
(more)
▼ An important phenomenon of systems driven far-from-equilibrium is spatiotemporal chaos where the dynamics are aperiodic in both time and space. We explored this numerically for three systems: the Lorenz-96 model, the Swift-Hohenberg equation, and Rayleigh-Bénard convection. The Lorenz-96 model is a continuous in time and discrete in space phenomenological model that captures important features of atmosphere dynamics. We computed the fractal dimension as a function of system size and external forcing to estimate characteristic length and time scales describing the chaotic dynamics. We found extensive chaos with significant deviations from extensivity for small changes in system size and also the power-law growth of the dimension with increasing forcing. The Swift-Hohenberg equation is a partial differential equation for a scalar field, which has been widely used as a model for the study of pattern formation. We found that the magnitude of the mean flow in this model must be sufficiently large for spiral defect chaos to occur. We also explored the spatiotemporal chaos in experimentally accessible Rayleigh-Bénard convection using large-scale numerical simulations of the Boussinesq equations and the corresponding tangent space equations. We performed a careful study analyzing the impact of variations in the domain size, Rayleigh number, and Prandtl number on the system dynamics and fractal dimension. In addition, we quantified the dynamics of the spectrum of Lyapunov exponents and the leading order Lyapunov vector in an effort to connect directly with the dynamics of the flow field patterns. Further, we numerically studied the synchronization of chaos in convective flows by imposing time-dependent boundary conditions from a principal domain onto an initially quiescent target domain. We identified a synchronization length scale to quantify the size of a chaotic element using only information from the pattern dynamics. We also explored the relationship of this length scale with the pattern wavelength. Finally, we analyzed bioconvection which occurs as the result of the collective behavior of a suspension of swimming microorganisms. We developed a series of simulations to capture the gyrotactic pattern formation of the swimming algae. The results can be compared with the corresponding trend of pattern instabilities observed in the experimental studies.
Advisors/Committee Members: Paul, Mark R. (committeechair), De Vita, Raffaella (committee member), Ross, Shane D. (committee member), Iliescu, Traian (committee member), Jung, Sunghwan (committee member).
Subjects/Keywords: Synchronization; Bioconvection; Spatiotemporal Chaos; Pattern Formation; Lyapunov Diagnostics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Karimi, A. (2012). Gaining New Insights into Spatiotemporal Chaos with Numerics. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/77347
Chicago Manual of Style (16th Edition):
Karimi, Alireza. “Gaining New Insights into Spatiotemporal Chaos with Numerics.” 2012. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/77347.
MLA Handbook (7th Edition):
Karimi, Alireza. “Gaining New Insights into Spatiotemporal Chaos with Numerics.” 2012. Web. 13 Apr 2021.
Vancouver:
Karimi A. Gaining New Insights into Spatiotemporal Chaos with Numerics. [Internet] [Doctoral dissertation]. Virginia Tech; 2012. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/77347.
Council of Science Editors:
Karimi A. Gaining New Insights into Spatiotemporal Chaos with Numerics. [Doctoral Dissertation]. Virginia Tech; 2012. Available from: http://hdl.handle.net/10919/77347
Virginia Tech
15.
Yu, Haofeng.
A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems.
Degree: PhD, Mathematics, 2011, Virginia Tech
URL: http://hdl.handle.net/10919/29095
► This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and…
(more)
▼ This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space.
The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions.
Advisors/Committee Members: Iliescu, Traian (committeechair), Burns, John A. (committee member), De Vita, Raffaella (committee member), Borggaard, Jeffrey T. (committee member).
Subjects/Keywords: Ericksenâ s Bar; Semi-linear Equations; Global Optimization; Canonical Duality Theory; Canonical Dual Finite Element Method; Landau-Ginzburg Problem.; Duality; Non-convex Variational Problems
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Yu, H. (2011). A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/29095
Chicago Manual of Style (16th Edition):
Yu, Haofeng. “A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems.” 2011. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/29095.
MLA Handbook (7th Edition):
Yu, Haofeng. “A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems.” 2011. Web. 13 Apr 2021.
Vancouver:
Yu H. A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems. [Internet] [Doctoral dissertation]. Virginia Tech; 2011. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/29095.
Council of Science Editors:
Yu H. A Numerical Investigation Of The Canonical Duality Method For Non-Convex Variational Problems. [Doctoral Dissertation]. Virginia Tech; 2011. Available from: http://hdl.handle.net/10919/29095
Virginia Tech
16.
San, Omer.
Multiscale Modeling and Simulation of Turbulent Geophysical Flows.
Degree: PhD, Engineering Science and Mechanics, 2012, Virginia Tech
URL: http://hdl.handle.net/10919/28031
► The accurate and efficient numerical simulation of geophysical flows is of great interest in numerical weather prediction and climate modeling as well as in numerous…
(more)
▼ The accurate and efficient numerical simulation of geophysical flows is of great interest in numerical weather prediction and climate modeling as well as in numerous critical areas and industries, such as agriculture, construction, tourism, transportation, weather-related disaster management, and sustainable energy technologies. Oceanic and atmospheric flows display an enormous range of temporal and spatial scales, from seconds to decades and from centimeters to thousands of kilometers, respectively. Scale interactions, both spatial and temporal, are the dominant feature of all aspects of general circulation models in geophysical fluid dynamics. In this thesis, to decrease the cost for these geophysical flow computations, several types of multiscale methods were systematically developed and tested for a variety of physical settings including barotropic and stratified wind-driven large scale ocean circulation models, decaying and forced two-dimensional turbulence simulations, as well as several benchmark incompressible flow problems in two and three dimensions. The new models proposed here are based on two classes of modern multiscale methods: (i) interpolation based approaches in the context of the multigrid/multiresolution methodologies, and (ii) deconvolution based spatial filtering approaches in the context of large eddy simulation techniques. In the first case, we developed a coarse-grid projection method that uses simple interpolation schemes to go between the two components of the problem, in which the solution algorithms have different levels of complexity. In the second case, the use of approximate deconvolution closure modeling strategies was implemented for large eddy simulations of large-scale turbulent geophysical flows. The numerical assessment of these approaches showed that both the coarse-grid projection and approximate deconvolution methods could represent viable tools for computing more realistic turbulent geophysical flows that provide significant increases in accuracy and computational efficiency over conventional methods.
Advisors/Committee Members: Staples, Anne E. (committeechair), Stremler, Mark A. (committee member), De Vita, Raffaella (committee member), Iliescu, Traian (committee member), Ragab, Saad A. (committee member).
Subjects/Keywords: Geophysical Flows; Physical Oceanography; Multiscale Modeling; Multigrid; Large Eddy Simulation; Computational Fluid Dynamics
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
San, O. (2012). Multiscale Modeling and Simulation of Turbulent Geophysical Flows. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/28031
Chicago Manual of Style (16th Edition):
San, Omer. “Multiscale Modeling and Simulation of Turbulent Geophysical Flows.” 2012. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/28031.
MLA Handbook (7th Edition):
San, Omer. “Multiscale Modeling and Simulation of Turbulent Geophysical Flows.” 2012. Web. 13 Apr 2021.
Vancouver:
San O. Multiscale Modeling and Simulation of Turbulent Geophysical Flows. [Internet] [Doctoral dissertation]. Virginia Tech; 2012. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/28031.
Council of Science Editors:
San O. Multiscale Modeling and Simulation of Turbulent Geophysical Flows. [Doctoral Dissertation]. Virginia Tech; 2012. Available from: http://hdl.handle.net/10919/28031
Virginia Tech
17.
Wang, Zhu.
Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations.
Degree: PhD, Mathematics, 2012, Virginia Tech
URL: http://hdl.handle.net/10919/27504
► Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational cost of direct numerical simulations, especially for three-dimensional nonlinear…
(more)
▼ Reduced-order models are frequently used in the simulation of complex flows to overcome the high computational cost of direct numerical simulations, especially for three-dimensional nonlinear problems.
Proper orthogonal decomposition, as one of the most commonly used tools to generate reduced-order models, has been utilized in many engineering and scientific applications.
Its original promise of computationally efficient, yet accurate approximation of coherent structures in high Reynolds number turbulent flows, however, still remains to be fulfilled. To balance the low computational cost required by reduced-order modeling and the complexity of the targeted flows, appropriate closure modeling strategies need to be employed.
In this dissertation, we put forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model.
These models, which are considered state-of-the-art in large eddy simulation, are carefully derived and numerically investigated.
Since modern closure models for turbulent flows generally have non-polynomial nonlinearities, their efficient numerical discretization within a proper orthogonal decomposition framework is challenging. This dissertation proposes a two-level method for an efficient and accurate numerical discretization of general nonlinear proper orthogonal decomposition closure models. This method computes the nonlinear terms of the reduced-order model on a coarse mesh. Compared with a brute force computational approach in which the nonlinear terms are evaluated on the fine mesh at each time step, the two-level method attains the same level of accuracy while dramatically reducing the computational cost. We numerically illustrate these improvements in the two-level method by using it in three settings: the one-dimensional Burgers equation with a small diffusion parameter, a two-dimensional flow past a cylinder at Reynolds number Re = 200, and a three-dimensional flow past a cylinder at Reynolds number Re = 1000.
With the help of the two-level algorithm, the new nonlinear proper orthogonal decomposition closure models (i.e., the dynamic subgrid-scale model and the variational multiscale model), together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a three-dimensional turbulent flow past a cylinder at Re = 1000. Five criteria are used to judge the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum, the mean velocity, the Reynolds stresses, the root mean square values of the velocity fluctuations, and the time evolution of the proper orthogonal decomposition basis coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models are the most accurate.
We present a rigorous numerical analysis for the…
Advisors/Committee Members: Iliescu, Traian (committeechair), Burns, John A. (committee member), Borggaard, Jeffrey T. (committee member), Lin, Tao (committee member), Zietsman, Lizette (committee member).
Subjects/Keywords: variational multiscale; dynamic subgrid-scale model; two-level algorithm; approximate deconvolution; finite elements; numerical analysis; Proper orthogonal decomposition; reduced-order modeling; large eddy simulation; eddy viscosity; turbulence
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wang, Z. (2012). Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/27504
Chicago Manual of Style (16th Edition):
Wang, Zhu. “Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations.” 2012. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/27504.
MLA Handbook (7th Edition):
Wang, Zhu. “Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations.” 2012. Web. 13 Apr 2021.
Vancouver:
Wang Z. Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations. [Internet] [Doctoral dissertation]. Virginia Tech; 2012. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/27504.
Council of Science Editors:
Wang Z. Reduced-Order Modeling of Complex Engineering and Geophysical Flows: Analysis and Computations. [Doctoral Dissertation]. Virginia Tech; 2012. Available from: http://hdl.handle.net/10919/27504
Virginia Tech
18.
Bishnoi, Hemant.
Behavioral EMI-Models of Switched Power Converters.
Degree: PhD, Electrical Engineering, 2013, Virginia Tech
URL: http://hdl.handle.net/10919/23936
► Measurement-based behavioral electromagnetic interference (EMI) models have been shown earlier to accurately capture the EMI behavior of switched power converters. These models are compact, linear,…
(more)
▼ Measurement-based behavioral electromagnetic interference (EMI) models have been shown earlier to accurately capture the EMI behavior of switched power converters. These models are compact, linear, and run in frequency domain, enabling faster and more stable simulations compared to the detailed lumped circuit models. So far, the behavioral EMI modeling techniques are developed and applied to the converter's input side only. The resulting models are therefore referred to as "terminated EMI models". Under the condition that the output side of the converter remains fixed, these models can predict the input side EMI for any change in the impedance of the input side network. However, any change at the output side would require re-extraction of the behavioral model. Thus the terminated EMI models are incapable of predicting the change in the input side EMI due to changes at the output side of the converter or vice versa.
The above mentioned limitation has been overcome by an "un-terminated EMI model" proposed in this dissertation. Un-terminated EMI models are developed here to predict both the common-mode (CM) and the differential (DM) noise currents at the input and the output sides of a motor-drive system. The modeling procedure itself has been simplified and now requires fewer measurements and results in less noise in the identified model parameters. Both CM and DM models are then combined to predict the total noise in the motor drive system. All models are validated by experiments and their limitations identified.
A significant portion of this dissertation is then devoted to the application of behavioral EMI models in the design of EMI filters. Comprehensive design procedures are developed for both DM and CM filters in a motor-drive system. The filters designed using the proposed methods are experimentally shown to satisfy the DO-160 conducted emissions standards.
The dissertation ends with a summary of contributions, limitations, and some future research directions.
Advisors/Committee Members: Boroyevich, Dushan (committeechair), Brown, Gary S. (committee member), Iliescu, Traian (committee member), Ngo, Khai D. (committee member), Mattavelli, Paolo (committee member).
Subjects/Keywords: conducted emissions; motor-drives; EMC; behavioral model; EMI filters
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Bishnoi, H. (2013). Behavioral EMI-Models of Switched Power Converters. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/23936
Chicago Manual of Style (16th Edition):
Bishnoi, Hemant. “Behavioral EMI-Models of Switched Power Converters.” 2013. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/23936.
MLA Handbook (7th Edition):
Bishnoi, Hemant. “Behavioral EMI-Models of Switched Power Converters.” 2013. Web. 13 Apr 2021.
Vancouver:
Bishnoi H. Behavioral EMI-Models of Switched Power Converters. [Internet] [Doctoral dissertation]. Virginia Tech; 2013. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/23936.
Council of Science Editors:
Bishnoi H. Behavioral EMI-Models of Switched Power Converters. [Doctoral Dissertation]. Virginia Tech; 2013. Available from: http://hdl.handle.net/10919/23936
Virginia Tech
19.
Foster, Erich Leigh.
Finite Elements for the Quasi-Geostrophic Equations of the Ocean.
Degree: PhD, Mathematics, 2013, Virginia Tech
URL: http://hdl.handle.net/10919/19362
► The quasi-geostrophic equations (QGE) are usually discretized in space by the finite difference method. The finite element (FE) method, however, offers several advantages over the…
(more)
▼ The quasi-geostrophic equations (QGE) are usually discretized in space by the finite difference method. The finite element (FE) method, however, offers several advantages over the finite difference method, such as the easy treatment of complex boundaries and a natural treatment of boundary conditions [Myers1995]. Despite these advantages, there are relatively few papers that consider the FE method applied to the QGE. Most FE discretizations of the QGE have been developed for the streamfunction-vorticity formulation. The reason is simple: The streamfunction-vorticity formulation yields a second order \\emph{partial differential equation (PDE)}, whereas the streamfunction formulation yields a fourth order PDE. Thus, although the streamfunction-vorticity formulation has two variables (q and \ψ) and the streamfunction formulation has just one (\ψ), the former is the preferred formulation used in practical computations, since its conforming FE discretization requires low-order (C
0) elements, whereas the latter requires a high-order (C
1) FE discretization. We present a conforming FE discretization of the QGE based on the Argyris element and we present a two-level FE discretization of the Stationary QGE (SQGE) based on the same conforming FE discretization using the Argyris element. We also, for the first time, develop optimal error estimates for the FE discretization QGE. Numerical tests for the FE discretization and the two-level FE discretization of the QGE are presented and theoretical error estimates are verified. By benchmarking the numerical results against those in the published literature, we conclude that our FE discretization is accurate. �Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates.
Advisors/Committee Members: Iliescu, Traian (committeechair), Adjerid, Slimane (committee member), Burns, John A. (committee member), Staples, Anne E. (committee member).
Subjects/Keywords: Quasi-geostrophic equations; finite element method; Argyris element; wind-driven ocean currents.
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Foster, E. L. (2013). Finite Elements for the Quasi-Geostrophic Equations of the Ocean. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/19362
Chicago Manual of Style (16th Edition):
Foster, Erich Leigh. “Finite Elements for the Quasi-Geostrophic Equations of the Ocean.” 2013. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/19362.
MLA Handbook (7th Edition):
Foster, Erich Leigh. “Finite Elements for the Quasi-Geostrophic Equations of the Ocean.” 2013. Web. 13 Apr 2021.
Vancouver:
Foster EL. Finite Elements for the Quasi-Geostrophic Equations of the Ocean. [Internet] [Doctoral dissertation]. Virginia Tech; 2013. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/19362.
Council of Science Editors:
Foster EL. Finite Elements for the Quasi-Geostrophic Equations of the Ocean. [Doctoral Dissertation]. Virginia Tech; 2013. Available from: http://hdl.handle.net/10919/19362
Virginia Tech
20.
Wells, David Reese.
Stabilization of POD-ROMs.
Degree: PhD, Mathematics, 2015, Virginia Tech
URL: http://hdl.handle.net/10919/52960
► This thesis describes several approaches for stabilizing POD-ROMs (that is, reduced order models based on basis functions derived from the proper orthogonal decomposition) for both…
(more)
▼ This thesis describes several approaches for stabilizing POD-ROMs
(that is, reduced order models based on basis functions derived from the proper
orthogonal decomposition) for both the CDR (convection-diffusion-reaction)
equation and the NSEs (Navier-Stokes equations). Stabilization is necessary
because standard POD-ROMs of convection-dominated problems usually display
numerical instabilities.
The first stabilized ROM investigated is a streamline-upwind
Petrov-Galerkin ROM (SUPG-ROM). I prove error estimates for the SUPG-ROM and
derive optimal scalings for the stabilization parameter. I test the SUPG-ROM
with the optimal parameter in the numerical simulation of a convection-dominated
CDR problem. The SUPG-ROM yields more accurate results than the standard
Galerkin ROM (G-ROM) by eliminating the inherent numerical artifacts (noise) in
the data and dampening spurious oscillations.
I next propose two regularized ROMs (Reg-ROMs) based on ideas from large
eddy simulation and turbulence theory: the Leray ROM (L-ROM) and the
evolve-then-filter ROM (EF-ROM). Both Reg-ROMs use explicit POD spatial
filtering to regularize (smooth) some of the terms in the standard G-ROM. I
propose two different POD spatial filters: one based on the POD projection and a
novel POD differential filter. These two new Reg-ROMs and the two spatial
filters are investigated in the numerical simulation of the three-dimensional
flow past a circular cylinder problem at Re = 100. The numerical results
show that EF-ROM-DF is the most accurate Reg-ROM and filter combination and the
differential filter generally yields better results than the projection filter.
The Reg-ROMs perform significantly better than the standard G-ROM and decrease
the CPU time (compared against the direct numerical simulation) by orders of
magnitude (from about four days to four minutes).
Advisors/Committee Members: Iliescu, Traian (committeechair), Glatt-Holtz, Nathan (committee member), Gugercin, Serkan (committee member), Paul, Mark R. (committee member).
Subjects/Keywords: Reduced Order Modeling; Proper Orthogonal Decomposition; Large Eddy Simulation; Regularized Models; Streamline-Upwind Petrov-Galerkin; Scientific Computing
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Wells, D. R. (2015). Stabilization of POD-ROMs. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/52960
Chicago Manual of Style (16th Edition):
Wells, David Reese. “Stabilization of POD-ROMs.” 2015. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/52960.
MLA Handbook (7th Edition):
Wells, David Reese. “Stabilization of POD-ROMs.” 2015. Web. 13 Apr 2021.
Vancouver:
Wells DR. Stabilization of POD-ROMs. [Internet] [Doctoral dissertation]. Virginia Tech; 2015. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/52960.
Council of Science Editors:
Wells DR. Stabilization of POD-ROMs. [Doctoral Dissertation]. Virginia Tech; 2015. Available from: http://hdl.handle.net/10919/52960
Virginia Tech
21.
Zhang, Hong.
Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations.
Degree: PhD, Computer Science and Applications, 2014, Virginia Tech
URL: http://hdl.handle.net/10919/50492
► Many fields in science and engineering require large-scale numerical simulations of complex systems described by differential equations. These systems are typically multi-physics (they are driven…
(more)
▼ Many fields in science and engineering require large-scale numerical simulations of complex systems described by differential equations. These systems are typically multi-physics (they are driven by multiple interacting physical processes) and multiscale (the dynamics takes place on vastly different spatial and temporal scales). Numerical solution of such systems is highly challenging due to the dimension of the resulting discrete problem, and to the complexity that comes from incorporating multiple interacting components with different characteristics. The main contributions of this dissertation are the creation of new families of time integration methods for multiscale and multiphysics simulations, and the development of industrial-strengh tools for sensitivity analysis.
This work develops novel implicit-explicit (IMEX) general linear time integration methods for multiphysics and multiscale simulations typically involving both stiff and non-stiff components. In an IMEX approach, one uses an implicit scheme for the stiff components and an explicit scheme for the non-stiff components such that the combined method has the desired stability and accuracy properties. Practical schemes with favorable properties, such as maximized stability, high efficiency, and no order reduction, are constructed and applied in extensive numerical experiments to validate the theoretical findings and to demonstrate their advantages. Approximate matrix factorization (AMF) technique exploits the structure of the Jacobian of the implicit parts, which may lead to further efficiency improvement of IMEX schemes. We have explored the application of AMF within some high order IMEX Runge-Kutta schemes in order to achieve high efficiency.
Sensitivity analysis gives quantitative information about the changes in a dynamical model outputs caused by caused by small changes in the model inputs. This information is crucial for data assimilation, model-constrained optimization, inverse problems, and uncertainty quantification. We develop a high performance software package for sensitivity analysis in the context of stiff and nonstiff ordinary differential equations. Efficiency is demonstrated by direct comparisons against existing state-of-art software on a variety of test problems.
Advisors/Committee Members: Sandu, Adrian (committeechair), Cao, Yang (committee member), Spiteri, Raymond John (committee member), Lin, Tao (committee member), Ribbens, Calvin J. (committee member), Iliescu, Traian (committee member).
Subjects/Keywords: Time Stepping; General Linear Methods; Implicit-explicit; Sensitivity Analysis
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zhang, H. (2014). Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/50492
Chicago Manual of Style (16th Edition):
Zhang, Hong. “Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations.” 2014. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/50492.
MLA Handbook (7th Edition):
Zhang, Hong. “Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations.” 2014. Web. 13 Apr 2021.
Vancouver:
Zhang H. Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations. [Internet] [Doctoral dissertation]. Virginia Tech; 2014. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/50492.
Council of Science Editors:
Zhang H. Efficient Time Stepping Methods and Sensitivity Analysis for Large Scale Systems of Differential Equations. [Doctoral Dissertation]. Virginia Tech; 2014. Available from: http://hdl.handle.net/10919/50492
22.
Nasr Azadani, Leila.
Advanced Spectral Methods for Turbulent Flows.
Degree: PhD, Engineering Mechanics, 2014, Virginia Tech
URL: http://hdl.handle.net/10919/47676
► Although spectral methods have been in use for decades, there is still room for innovation, refinement and improvement of the methods in terms of efficiency…
(more)
▼ Although spectral methods have been in use for decades, there is still room for innovation, refinement and improvement of the methods in terms of efficiency and accuracy, for generalized homogeneous turbulent flows, and especially for specialized applications like the computation of atmospheric flows and numerical weather prediction. In this thesis, two such innovations are presented. First, inspired by the adaptive mesh refinement (AMR) technique, which was developed for the computation of fluid flows in physical space, an algorithm is presented for accelerating direct numerical simulation (DNS) of isotropic homogeneous turbulence in spectral space. In the adaptive spectral resolution (ASR) technique developed here the spectral resolution in spectral space is dynamically refined based on refinement criteria suited to the special features of isotropic homogeneous turbulence in two, and three dimensions. Applying ASR to computations of two- and three-dimensional turbulence allows significant savings in the computational time with little to no compromise in the accuracy of the solutions. In the second part of this thesis the effect of explicit filtering on large eddy simulation (LES) of atmospheric flows in spectral space is studied. Apply an explicit filter in addition to the implicit filter due to the computational grid and discretization schemes in LES of turbulent flows allows for better control of the numerical error and improvement in the accuracy of the results. Explicit filtering has been extensively applied in LES of turbulent flows in physical space while few studies have been done on explicitly filtered LES of turbulent flows in spectral space because of perceived limitations of the approach, which are shown here to be incorrect. Here, explicit filtering in LES of the turbulent barotropic vorticity equation (BVE) as a first model of the Earth's atmosphere in spectral space is studied. It is shown that explicit filtering increases the accuracy of the results over implicit filtering, particularly where the location of coherent structures is concerned.
Advisors/Committee Members: Staples, Anne E. (committeechair), Paul, Mark R. (committee member), Iliescu, Traian (committee member), Tafti, Danesh K. (committee member), Ross, Shane D. (committee member).
Subjects/Keywords: Turbulent Flows; Spectral Methods; Large Eddy Simulation; Direct Numerical Simulation
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Nasr Azadani, L. (2014). Advanced Spectral Methods for Turbulent Flows. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/47676
Chicago Manual of Style (16th Edition):
Nasr Azadani, Leila. “Advanced Spectral Methods for Turbulent Flows.” 2014. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/47676.
MLA Handbook (7th Edition):
Nasr Azadani, Leila. “Advanced Spectral Methods for Turbulent Flows.” 2014. Web. 13 Apr 2021.
Vancouver:
Nasr Azadani L. Advanced Spectral Methods for Turbulent Flows. [Internet] [Doctoral dissertation]. Virginia Tech; 2014. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/47676.
Council of Science Editors:
Nasr Azadani L. Advanced Spectral Methods for Turbulent Flows. [Doctoral Dissertation]. Virginia Tech; 2014. Available from: http://hdl.handle.net/10919/47676
Virginia Tech
23.
Baccouch, Mahboub.
Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes.
Degree: PhD, Mathematics, 2008, Virginia Tech
URL: http://hdl.handle.net/10919/26331
► In this thesis, we present new superconvergence properties of discontinuous Galerkin (DG) methods for two-dimensional hyperbolic problems. We investigate the superconvergence properties of the DG…
(more)
▼ In this thesis, we present new superconvergence properties of discontinuous Galerkin (DG) methods for two-dimensional hyperbolic problems. We investigate the superconvergence properties of the DG method applied to scalar first-order hyperbolic partial differential equations on triangular meshes. We study the effect of finite element spaces on the superconvergence properties of DG solutions on three types of triangular elements. Superconvergence is described for structured and unstructured meshes. We show that the DG solution is O(hp+1) superconvergent at Legendre points on the outflow edge on triangles having one outflow edge using three p- degree polynomial spaces. For triangles having two outflow edges the finite element error is O(hp+1) superconvergent at the end points of the inflow edge for an augmented space of degree p. Furthermore, we discovered additional mesh-orientation dependent superconvergence points in the interior of triangles. The dependence of these points on orientation is explicitly given. We also established a global superconvergence result on meshes consisting of triangles having one inflow and one outflow edges.
Applying a local error analysis, we construct simple, efficient and asymptotically correct a posteriori error estimates for discontinuous finite element solutions of hyperbolic problems on triangular meshes. A posteriori error estimates are needed to guide adaptive enrichment and to provide a measure of solution accuracy for any numerical method. We develop an inexpensive superconvergence-based a posteriori error estimation technique for the DG solutions of conservation laws. We explicitly write the basis functions for the error spaces corresponding to several finite element solution spaces. The leading term of the discretization error on each triangle is estimated by solving a local problem where no boundary conditions are needed. The computed error estimates are shown to converge to the true error under mesh refinement in smooth solution regions. We further present a numerical study of superconvergence properties for the DG method applied to time-dependent convection problems. We also construct asymptotically correct a posteriori error estimates by solving local hyperbolic problems with no boundary conditions on general unstructured meshes. The global superconvergence results are numerically confirmed. Finally, the a posteriori error estimates are tested on several linear and nonlinear problems to show their efficiency and accuracy under mesh refinement.
Advisors/Committee Members: Adjerid, Slimane (committeechair), Sun, Shu-Ming (committee member), Iliescu, Traian (committee member), Lin, Tao (committee member).
Subjects/Keywords: hyperbolic problems; a posteriori errorestimates; Discontinuous Galerkin method; triangular meshes; superconvergence
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Baccouch, M. (2008). Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/26331
Chicago Manual of Style (16th Edition):
Baccouch, Mahboub. “Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes.” 2008. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/26331.
MLA Handbook (7th Edition):
Baccouch, Mahboub. “Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes.” 2008. Web. 13 Apr 2021.
Vancouver:
Baccouch M. Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes. [Internet] [Doctoral dissertation]. Virginia Tech; 2008. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/26331.
Council of Science Editors:
Baccouch M. Superconvergence and A posteriori Error Estimation for the Discontinuous Galerkin Method Applied to Hyperbolic Problems on Triangular Meshes. [Doctoral Dissertation]. Virginia Tech; 2008. Available from: http://hdl.handle.net/10919/26331
Virginia Tech
24.
Hou, Peter S.
Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems.
Degree: MS, Mathematics, 2005, Virginia Tech
URL: http://hdl.handle.net/10919/32026
► The availability of high performance computing clusters has allowed scientists and engineers to study more challenging problems. However, new algorithms need to be developed to…
(more)
▼ The availability of high performance computing clusters has allowed scientists and engineers to study more challenging problems. However, new algorithms need to be developed to take advantage of the new computer architecture (in particular, distributed memory clusters). Since the solution of linear systems still demands most of the computational effort in many problems (such as the approximation of partial differential equation models) iterative methods and, in particular, efficient preconditioners need to be developed.
In this study, we consider application of incomplete LU (ILU) preconditioners for finite element models to partial differential equations. Since finite elements lead to large, sparse systems, reordering the node numbers can have a substantial influence on the effectiveness of these preconditioners. We study two implementations of the ILU preconditioner: a stucturebased method and a threshold-based method. The main emphasis of the thesis is to test a variety of breadth-first ordering strategies on the convergence properties of the preconditioned systems. These include conventional Cuthill-McKee (CM) and Reverse Cuthill-McKee (RCM) orderings as well as strategies related to the physical distance between nodes and post-processing methods based on relative sizes of associated matrix entries. Although the success of these methods were problem dependent, a number of tendencies emerged from which we could make recommendations. Finally, we perform a preliminary study of the multi-processor case and observe the importance of partitioning quality and the parallel ILU reordering strategy.
Advisors/Committee Members: Borggaard, Jeffrey T. (committeechair), Iliescu, Traian (committee member), Gugercin, Serkan (committee member).
Subjects/Keywords: Iterative Solver; Scientific Computing; Unstructured Mesh; Finite Element Method; Preconditioner; Nodal Reordering Strategy
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Hou, P. S. (2005). Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/32026
Chicago Manual of Style (16th Edition):
Hou, Peter S. “Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems.” 2005. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/32026.
MLA Handbook (7th Edition):
Hou, Peter S. “Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems.” 2005. Web. 13 Apr 2021.
Vancouver:
Hou PS. Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems. [Internet] [Masters thesis]. Virginia Tech; 2005. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/32026.
Council of Science Editors:
Hou PS. Nodal Reordering Strategies to Improve Preconditioning for Finite Element Systems. [Masters Thesis]. Virginia Tech; 2005. Available from: http://hdl.handle.net/10919/32026
Virginia Tech
25.
O'Connor, Nicholas L.
The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer.
Degree: MS, Mechanical Engineering, 2008, Virginia Tech
URL: http://hdl.handle.net/10919/32705
► The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail.…
(more)
▼ The nonlinear and chaotic dynamics of a shallow fluid layer are investigated numerically using large-scale parallel numerical simulations. Two particular situations are studied in detail. First, a fluid layer is placed between rigid boundaries and heated from below to yield the chaotic dynamics of thermal convection rolls (Rayleigh-Bénard convection). Second is a free-surface fluid layer placed on a shaker to yield nonlinear surface waves (Faraday waves). In both cases the full governing partial differential equations are solved using parallel spectral element methods.
Rayleigh-Bénard convection is studied in a cylindrical dish with realistic boundaries. The complete flow field is obtained as well as the spectrum of Lyapunov exponents and Lyapunov vectors. The Lyapunov exponents and their corresponding perturbation fields are used to determine when and where events occur that contribute most to the chaotic dynamics. Roll pinch-off and roll mergers are found to be the largest contributors.
Two dimensional and three dimensional Faraday waves are studied with periodic boundary conditions. The full Navier-Stokes equations are solved including the complex dynamics of the free surface waves to gain a better understanding of the interplay between the viscous boundary layers, the nonlinear streaming flow, and the bulk flow. The vortices in the bulk flow are weak compared to the flow in the viscous boundary layers. The surface waves are found to be non-sinusoidal and the time evolution of the waves are explored for both large and small amplitude waves.
Advisors/Committee Members: Paul, Mark R. (committeechair), Tafti, Danesh K. (committee member), Iliescu, Traian (committee member).
Subjects/Keywords: Boussinesq; Spatiotemporal; Chaos
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
O'Connor, N. L. (2008). The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/32705
Chicago Manual of Style (16th Edition):
O'Connor, Nicholas L. “The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer.” 2008. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/32705.
MLA Handbook (7th Edition):
O'Connor, Nicholas L. “The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer.” 2008. Web. 13 Apr 2021.
Vancouver:
O'Connor NL. The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer. [Internet] [Masters thesis]. Virginia Tech; 2008. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/32705.
Council of Science Editors:
O'Connor NL. The Complex Spatiotemporal Dynamics of a Shallow Fluid Layer. [Masters Thesis]. Virginia Tech; 2008. Available from: http://hdl.handle.net/10919/32705
Virginia Tech
26.
Kovacs, Denis Christoph.
Inertial Manifolds and Nonlinear Galerkin Methods.
Degree: MS, Mathematics, 2005, Virginia Tech
URL: http://hdl.handle.net/10919/30792
► Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term…
(more)
▼ Nonlinear Galerkin methods utilize approximate inertial manifolds to reduce the spatial error of the standard Galerkin method. For certain scenarios, where a rough forcing term is used, a simple postprocessing step yields the same improvements that can be observed with nonlinear Galerkin. We show that this improvement is mainly due to the information about the forcing term that is neglected by standard Galerkin. Moreover, we construct a simple postprocessing scheme that uses only this neglected information but gives the same increase in accuracy as nonlinear or postprocessed Galerkin methods.
Advisors/Committee Members: Borggaard, Jeffrey T. (committeechair), Gugercin, Serkan (committee member), Iliescu, Traian (committee member), Beattie, Christopher A. (committeecochair).
Subjects/Keywords: inertial manifolds; nonlinear Galerkin; postprocessed Galerkin; approximate inertial manifolds
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Kovacs, D. C. (2005). Inertial Manifolds and Nonlinear Galerkin Methods. (Masters Thesis). Virginia Tech. Retrieved from http://hdl.handle.net/10919/30792
Chicago Manual of Style (16th Edition):
Kovacs, Denis Christoph. “Inertial Manifolds and Nonlinear Galerkin Methods.” 2005. Masters Thesis, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/30792.
MLA Handbook (7th Edition):
Kovacs, Denis Christoph. “Inertial Manifolds and Nonlinear Galerkin Methods.” 2005. Web. 13 Apr 2021.
Vancouver:
Kovacs DC. Inertial Manifolds and Nonlinear Galerkin Methods. [Internet] [Masters thesis]. Virginia Tech; 2005. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/30792.
Council of Science Editors:
Kovacs DC. Inertial Manifolds and Nonlinear Galerkin Methods. [Masters Thesis]. Virginia Tech; 2005. Available from: http://hdl.handle.net/10919/30792
Virginia Tech
27.
Krueger, Denise A.
Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations.
Degree: PhD, Mathematics, 2004, Virginia Tech
URL: http://hdl.handle.net/10919/11214
► We study the behavior of numerical stabilization schemes in the context of linear quadratic regulator (LQR) control problems for convection diffusion equations. The motivation for…
(more)
▼ We study the behavior of numerical stabilization schemes in the context of linear quadratic regulator (LQR) control problems for convection diffusion equations. The motivation for this effort comes from the observation that when linearization is applied to fluid flow control problems the resulting equations have the form of a convection diffusion equation. This effort is focused on the specific problem of computing the feedback functional gains that are the kernels of the feedback operators defined by solutions of operator Riccati equations. We develop a stabilization scheme based on the Galerkin Least Squares (GLS) method and compare this scheme to the standard Galerkin finite element method. We use cubic B-splines in order to keep the higher order terms that occur in GLS formulation. We conduct a careful numerical investigation into the convergence and accuracy of the functional gains computed using stabilization. We also conduct numerical studies of the role that the stabilization parameter plays in this convergence. Overall, we discovered that stabilization produces much better approximations to the functional gains on coarse meshes than the unstabilized method and that adjustments in the stabilization parameter greatly effects the accuracy and convergence rates. We discovered that the optimal stabilization parameter for simulation and steady state analysis is not necessarily optimal for solving the Riccati equation that defines the functional gains. Finally, we suggest that the stabilized GLS method might provide good initial values for iterative schemes on coarse meshes.
Advisors/Committee Members: King, Belinda B. (committeechair), Burns, John A. (committee member), Borggaard, Jeffrey T. (committee member), Iliescu, Traian (committee member), Zietsman, Lizette (committee member).
Subjects/Keywords: Stabilized Finite Elements; Convection-Diffusion Equation; Linear Quadratic Regulator Problems; Non-normal
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Krueger, D. A. (2004). Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/11214
Chicago Manual of Style (16th Edition):
Krueger, Denise A. “Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations.” 2004. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/11214.
MLA Handbook (7th Edition):
Krueger, Denise A. “Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations.” 2004. Web. 13 Apr 2021.
Vancouver:
Krueger DA. Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations. [Internet] [Doctoral dissertation]. Virginia Tech; 2004. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/11214.
Council of Science Editors:
Krueger DA. Stabilized Finite Element Methods for Feedback Control of Convection Diffusion Equations. [Doctoral Dissertation]. Virginia Tech; 2004. Available from: http://hdl.handle.net/10919/11214
Virginia Tech
28.
Constantinescu, Emil Mihai.
Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation.
Degree: PhD, Computer Science, 2008, Virginia Tech
URL: http://hdl.handle.net/10919/27938
► Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are…
(more)
▼ Numerical simulation is necessary to understand natural phenomena, make assessments and predictions in various research and engineering fields, develop new technologies, etc. New algorithms are needed to take advantage of the increasing computational resources and utilize the emerging hardware and software infrastructure with maximum efficiency.
Adaptive numerical discretization methods can accommodate problems with various physical, scale, and dynamic features by adjusting the resolution, order, and the type of method used to solve them. In applications that simulate real systems, the numerical accuracy of the solution is typically just one of the challenges. Measurements can be included in the simulation to constrain the numerical solution through a process called data assimilation in order to anchor the simulation in reality.
In this thesis we investigate adaptive discretization methods and data assimilation approaches for large-scale numerical simulations. We develop and investigate novel multirate and implicit-explicit methods that are appropriate for multiscale and multiphysics numerical discretizations. We construct and explore data assimilation approaches for, but not restricted to, atmospheric chemistry applications. A generic approach for describing the structure of the uncertainty in initial conditions that can be applied to the most popular data assimilation approaches is also presented.
We show that adaptive numerical methods can effectively address the discretization of large-scale problems. Data assimilation complements the adaptive numerical methods by correcting the numerical solution with real measurements. Test problems and large-scale numerical experiments validate the theoretical findings. Synergistic approaches that use adaptive numerical methods within a data assimilation framework need to be investigated in the future.
Advisors/Committee Members: Sandu, Adrian (committeechair), Iliescu, Traian (committee member), Ryan, Jennifer K. (committee member), Santos, Eunice E. (committee member), Ribbens, Calvin J. (committee member), Watson, Layne T. (committee member).
Subjects/Keywords: data assimilation; IMEX; multirate; ODE and PDE time integration
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Constantinescu, E. M. (2008). Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/27938
Chicago Manual of Style (16th Edition):
Constantinescu, Emil Mihai. “Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation.” 2008. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/27938.
MLA Handbook (7th Edition):
Constantinescu, Emil Mihai. “Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation.” 2008. Web. 13 Apr 2021.
Vancouver:
Constantinescu EM. Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation. [Internet] [Doctoral dissertation]. Virginia Tech; 2008. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/27938.
Council of Science Editors:
Constantinescu EM. Adaptive Numerical Methods for Large Scale Simulations and Data Assimilation. [Doctoral Dissertation]. Virginia Tech; 2008. Available from: http://hdl.handle.net/10919/27938
Virginia Tech
29.
Singler, John.
Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow.
Degree: PhD, Mathematics, 2005, Virginia Tech
URL: http://hdl.handle.net/10919/28051
► For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However,…
(more)
▼ For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows, this approach has failed to match experimental results. Recently, new scenarios for transition have been proposed that are based on the non-normality of the linearized operator. These new â mostly linearâ theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored. The main goal of this work is to begin to study the role of nonlinearity in transition. We use model problems to illustrate that small unmodeled disturbances can cause transition through movement or bifurcation of equilibria. We also demonstrate that small wall roughness can lead to transition by causing the linearized system to become unstable. Sensitivity methods are used to obtain important information about the disturbed problem and to illustrate that it is possible to have a precursor to predict transition. Finally, we apply linear feedback control to the model problems to illustrate the power of feedback to delay transition and even relaminarize fully developed chaotic flows.
Advisors/Committee Members: Burns, John A. (committeechair), Cliff, Eugene M. (committee member), Borggaard, Jeffrey T. (committee member), Iliescu, Traian (committee member), Herdman, Terry L. (committee member).
Subjects/Keywords: Sensitivity Analysis; Small Disturbances; Transition to Turbulence; Partial Differential Equations
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Singler, J. (2005). Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/28051
Chicago Manual of Style (16th Edition):
Singler, John. “Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow.” 2005. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/28051.
MLA Handbook (7th Edition):
Singler, John. “Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow.” 2005. Web. 13 Apr 2021.
Vancouver:
Singler J. Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow. [Internet] [Doctoral dissertation]. Virginia Tech; 2005. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/28051.
Council of Science Editors:
Singler J. Sensitivity Analysis of Partial Differential Equations With Applications to Fluid Flow. [Doctoral Dissertation]. Virginia Tech; 2005. Available from: http://hdl.handle.net/10919/28051
Virginia Tech
30.
Singh, Kumaresh.
Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation.
Degree: PhD, Computer Science, 2010, Virginia Tech
URL: http://hdl.handle.net/10919/39125
► The overall goals of this dissertation are to advance the field of chemical data assimilation, and to develop efficient computational tools that allow the atmospheric…
(more)
▼ The overall goals of this dissertation are to advance the field of chemical data assimilation, and to develop efficient computational tools that allow the atmospheric science community benefit from state of the art assimilation methodologies. Data assimilation is the procedure to combine data from observations with model predictions to obtain a more accurate representation of the state of the atmosphere.
As models become more complex, determining the relationships between pollutants and their sources and sinks becomes computationally more challenging. The construction of an adjoint model ( capable of efficiently computing sensitivities of a few model outputs with respect to many input parameters ) is a difficult, labor intensive, and error prone task. This work develops adjoint systems for two of the most widely used chemical transport models: Harvardâ s GEOS-Chem global model and for Environmental Protection Agencyâ s regional CMAQ regional air quality model. Both GEOS-Chem and CMAQ adjoint models are now used by the atmospheric science community to perform sensitivity analysis and data assimilation studies.
Despite the continuous increase in capabilities, models remain imperfect and models alone cannot provide accurate long term forecasts. Observations of the atmospheric composition are now routinely taken from sondes, ground stations, aircraft, and satellites, etc. This work develops three and four dimensional variational data assimilation capabilities for GEOS-Chem and CMAQ which allow to estimate chemical states that best fit the observed reality.
Most data assimilation systems to date use diagonal approximations of the background covariance matrix which ignore error correlations and may lead to inaccurate estimates. This dissertation develops computationally efficient representations of covariance matrices that allow to capture spatial error correlations in data assimilation.
Not all observations used in data assimilation are of equal importance. Erroneous and redundant observations not only affect the quality of an estimate but also add unnecessary computational expense to the assimilation system. This work proposes techniques to quantify the information content of observations used in assimilation; information-theoretic metrics are used.
The four dimensional variational approach to data assimilation provides accurate estimates but requires an adjoint construction, and uses considerable computational resources. This work studies versions of the four dimensional variational methods (Quasi 4D-Var) that use approximate gradients and are less expensive to develop and run.
Variational and Kalman filter approaches are both used in data assimilation, but their relative merits and disadvantages in the context of chemical data assimilation have not been assessed. This work provides a careful comparison on a chemical assimilation problem with real data sets. The assimilation experiments performed here demonstrate for the first time the benefit of using satellite data to improve estimates of tropospheric ozone.
Advisors/Committee Members: Sandu, Adrian (committeechair), Bowman, Kevin W. (committee member), Ribbens, Calvin J. (committee member), Cao, Yang (committee member), Iliescu, Traian (committee member), Feng, Wu-Chun (committeecochair).
Subjects/Keywords: Information Theory; Chemical Transport Models; Global Ozone Measurements; Model Adjoint Construction; Adjoint Sensitivity Analysis; Error Covariance Matrices; Data Assimilation
Record Details
Similar Records
Cite
Share »
Record Details
Similar Records
Cite
« Share
❌
APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Singh, K. (2010). Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/39125
Chicago Manual of Style (16th Edition):
Singh, Kumaresh. “Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation.” 2010. Doctoral Dissertation, Virginia Tech. Accessed April 13, 2021.
http://hdl.handle.net/10919/39125.
MLA Handbook (7th Edition):
Singh, Kumaresh. “Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation.” 2010. Web. 13 Apr 2021.
Vancouver:
Singh K. Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation. [Internet] [Doctoral dissertation]. Virginia Tech; 2010. [cited 2021 Apr 13].
Available from: http://hdl.handle.net/10919/39125.
Council of Science Editors:
Singh K. Efficient Computational Tools for Variational Data Assimilation and Information Content Estimation. [Doctoral Dissertation]. Virginia Tech; 2010. Available from: http://hdl.handle.net/10919/39125
◁ [1] [2] ▶
. 
Open Access Theses and Dissertations
