+publisher:"University of Texas – Austin" +contributor:("Arbogast, Todd")

1. Xiao, Hailong. Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media.

Degree: PhD, Computational and Applied Mathematics, 2013, University of Texas – Austin

URL: http://hdl.handle.net/2152/23317

► We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic… (more)

▼ We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))², which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor).

Subjects/Keywords: Porous medium; Elliptic system; Heterogeneous; Mixed finite element; Homogenization theory; Mortar method; Multiscale; Preconditioner; Slightly compressible single phase; Two-phase

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APA (6^th Edition):

Xiao, H. (2013). Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/23317

Chicago Manual of Style (16^th Edition):

Xiao, Hailong. “Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media.” 2013. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/23317.

MLA Handbook (7^th Edition):

Xiao, Hailong. “Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media.” 2013. Web. 18 Jan 2021.

Vancouver:

Xiao H. Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2013. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/23317.

Council of Science Editors:

Xiao H. Multiscale mortar mixed finite element methods for flow problems in highly heterogeneous porous media. [Doctoral Dissertation]. University of Texas – Austin; 2013. Available from: http://hdl.handle.net/2152/23317

University of Texas – Austin

2. Rabidoux, Scott Michael. Extending the reach of algorithms for the calculation of molecular vibronic spectra.

Degree: PhD, Computational science, engineering, and mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/44604

► Theoretical spectroscopy is an important field of chemistry that can help extract useful information about the properties of a molecule from experimental spectral data. Ab… (more)

▼ Theoretical spectroscopy is an important field of chemistry that can help extract useful information about the properties of a molecule from experimental spectral data. Ab initio calculations of molecular spectra can be performed and compared against experimental data to determine the validity of various calculated molecular properties. Unfortunately, the computational cost of these spectral simulations rises quickly with the number of atoms in the molecule of interest. As a result, current techniques for simulating molecular spectra are often limited for use with only the smallest of molecules. The main purpose of this work is to develop new computational tools in an effort to extend the reach of current state-of-the-art spectral simulation algorithms and allow for the spectroscopic study of larger molecules than is currently feasible. The calculation of vibronic spectra requires the solution of the time-independent Schrödinger equation to obtain the vibronic energy levels of a molecule and their corresponding transition intensities. When the Born-Oppenheimer approximation is applicable for the solution of the time-independent Schrödinger equation, the vibrational energy levels of a molecule can be easily determined analytically, if the harmonic approximation is used. What remains, then, for a spectral simulation, is the calculation of the transition intensities associated with each energy level. Under the harmonic approximation, the transition intensities (also known as Franck-Condon factors) can be calculated via a set of recurrence equations developed by Doktorov, Malkin, and Manko. The implementation of these recurrence equations, though, can be computationally intensive for medium-to-large molecules, especially for finite-temperature simulations. In this work, I present a new algorithm for the calculation of Franck-Condon factors via the Doktorov recurrence equations that achieves significantly better computational performance than existing implementations, with speedups of roughly thirty times on a single processor. When the Born-Oppenheimer approximation is not applicable, vibronic coupling effects must be accounted for to achieve an accurate spectral simulation. A common approach for treating vibronic coupling effects is to solve the time-independent Schrödinger equation using a model Hamiltonian developed by Köppel, Domcke, and Cederbaum (KDC). Using the KDC approach, the problem of solving the Schrödinger equation becomes a problem of solving for the eigenstates of a large, sparse matrix. The computational difficulty of this problem is then dependent on the size of the matrix. Unfortunately, the size of the matrix at hand grows exponentially with the number of vibrational modes of the molecule of interest, and matrix dimensions can easily reach upwards of one billion and beyond. In an attempt to make tractable problems involving very large matrices, I present in this work a distributed-memory parallelization strategy for the KDC approach. The resulting parallel algorithm achieves impressive parallel… Advisors/Committee Members: Stanton, John (John F.) (advisor), Eijkhout, Victor (advisor), Arbogast, Todd (committee member), van de Geijn, Robert (committee member), Makarov, Dmitrii (committee member).

Subjects/Keywords: Computational spectroscopy; Vibronic coupling; High-performance computing; Franck-Condon; Butadiene

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APA (6^th Edition):

Rabidoux, S. M. (2016). Extending the reach of algorithms for the calculation of molecular vibronic spectra. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/44604

Chicago Manual of Style (16^th Edition):

Rabidoux, Scott Michael. “Extending the reach of algorithms for the calculation of molecular vibronic spectra.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/44604.

MLA Handbook (7^th Edition):

Rabidoux, Scott Michael. “Extending the reach of algorithms for the calculation of molecular vibronic spectra.” 2016. Web. 18 Jan 2021.

Vancouver:

Rabidoux SM. Extending the reach of algorithms for the calculation of molecular vibronic spectra. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/44604.

Council of Science Editors:

Rabidoux SM. Extending the reach of algorithms for the calculation of molecular vibronic spectra. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/44604

University of Texas – Austin

3. Yang, Shan. A shape Hessian-based analysis of roughness effects on fluid flows.

Degree: PhD, Computational and Applied Mathematics, 2011, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2011-08-4036

► The flow of fluids over solid surfaces is an integral part of many technologies, and the analysis of such flows is important to the design… (more)

▼ The flow of fluids over solid surfaces is an integral part of many technologies, and the analysis of such flows is important to the design and operation of these technologies. Solid surfaces, however, are generally rough at some scale, and analyzing the effects of such roughness on fluid flows represents a significant challenge. There are two fluid flow situations in which roughness is particularly important, because the fluid shear layers they create can be very thin, of order the height of the roughness. These are very high Reynolds number turbulent wall-bounded flows (the viscous wall layer is very thin), and very low Reynolds number lubrication flows (the lubrication layer between moving surfaces is very thin). Analysis in both of these flow domains has long accounted for roughness through empirical adjustments to the smooth-wall analysis, with empirical parameters describing the fluid dynamic roughness effects. The ability to determine these effects from a topographic description of the roughness is limited (lubrication) or non-existent (turbulence). The commonly used parameter, the equivalent sand grain roughness, can be determined in terms of the change in the rate of viscous energy dissipation caused by the roughness and is generally obtained by measuring the effects on a fluid flow. However, determining fluid dynamic effects from roughness characteristics is critical to effective engineering analysis. Characterization of this mapping from roughness topography to fluid dynamic impact is the main topic of the dissertation. Using the mathematical tools of shape calculus, we construct this mapping by defining the roughness functional and derive its first- and second- order shape derivatives, i.e., the derivatives of the roughness functional with respect to the roughness topography. The results of the shape gradient and complete spectrum of the shape Hessian are presented for the low Reynolds number lubrication flows. Flow predictions based on this derivative information is shown to be very accurate for small roughness. However, for the study of high Reynolds number turbulent flows, the direct extension of the current approach fails due to the chaotic nature of turbulent flows. Challenges and possible approaches are discussed for the turbulence problem as well as a model problem, the sensitivity analysis of the Lorenz system. Advisors/Committee Members: Ghattas, Omar N. (advisor), Moser, Robert deLancey (advisor), Arbogast, Todd (committee member), Goldstein, David (committee member), Ying, Lexing (committee member).

Subjects/Keywords: Roughness analysis; Shape calculus; Navier-Stokes flow

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APA (6^th Edition):

Yang, S. (2011). A shape Hessian-based analysis of roughness effects on fluid flows. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-08-4036

Chicago Manual of Style (16^th Edition):

Yang, Shan. “A shape Hessian-based analysis of roughness effects on fluid flows.” 2011. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2011-08-4036.

MLA Handbook (7^th Edition):

Yang, Shan. “A shape Hessian-based analysis of roughness effects on fluid flows.” 2011. Web. 18 Jan 2021.

Vancouver:

Yang S. A shape Hessian-based analysis of roughness effects on fluid flows. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2011. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4036.

Council of Science Editors:

Yang S. A shape Hessian-based analysis of roughness effects on fluid flows. [Doctoral Dissertation]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-08-4036

University of Texas – Austin

4. Chen, Peila. Enhanced oil recovery in fractured vuggy carbonates.

Degree: PhD, Petroleum Engineering, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/31396

► Naturally fractured carbonates contribute substantially to global oil reserves. Waterflood and gas-oil gravity drainage (GOGD) recover oil from the fractured oil-wet carbonates, with limited success… (more)

▼ Naturally fractured carbonates contribute substantially to global oil reserves. Waterflood and gas-oil gravity drainage (GOGD) recover oil from the fractured oil-wet carbonates, with limited success due to poor sweep and very low recovery factors. Surfactant flooding has shown a great potential to enhance oil recovery in the oil-wet carbonates by reducing interfacial tension and/or altering wettability. Carbonates are characterized by the wide pore-size distributions. Surfactant EOR cannot be successfully implemented in a fractured, oil-wet, carbonate reservoir unless the reservoir is fully characterized and all of the mechanisms involved in oil recovery are fully understood. NMR T₂ measurement, mercury injection capillary pressure test (MICP), thin-section imaging, and computerized tomography (CT) scanning were conducted in the characterization of vuggy dolomite cores from the field. Both thin section and CT images reveal that the touching vugs and separate vugs co-exist in the core samples. Although the vuggy porosity is estimated to be 85%, the matrix controls the permeability of the core because of poor vug connectivity. MICP and NMR T₂ measurements show multimodal pore-throat and pore-body size distributions. Reconstructed 3D CT porosity maps indicate that the vugs in the field dolomite are large and randomly distributed, while the vugs in the Silurian dolomite are small and densely populated. A single-phase tracer test performed under CT scanner reveals a large porosity variation and the preferential flow paths within the field dolomite core. The mercury withdrawal test and NMR T₂ measurement have indicated that snap-off retains oil in the vugs due to the large aspect ratio pores and the large length-scale of the oil blobs. The imbibition oil recovery from the initially oil-wet field dolomite core is 20% lower (in OOIP) than that from the Silurian dolomite core, mainly because of an unfavorable pore structure in the field dolomite core. A few surfactants were selected as promising candidates for wettability alteration because they possess aqueous stability in hard brine at elevated temperatures and reduce contact angles. The divalent cations in the hard brine significantly suppress the anionic surfactant-mediated wettability alteration. The removal of Ca²⁺, and then Mg²⁺ from the hard brine progressively promotes anionic surfactant-assisted wettability alteration, evidenced by decreasing contact angles. The addition of sufficient amount of divalent ion scavengers, including chelating agents (e.g. EDTA.4Na) and scale inhibitors (e.g. Sodium Polyacrylate) in the hard brine, rescues the anionic surfactant-mediated wettability alteration. We propose that the scavenger reduces the concentration of free divalent cations, and promotes the release of the surfactant monomers, which favors wettability alteration through the surfactant adsorption mechanism. The scavenger- triggered mineral dissolution only weakly contributes to the imbibition oil recovery. Experiments and simulation studies consistently showed the… Advisors/Committee Members: Mohanty, Kishore Kumar (advisor), Pope, Gary A. (committee member), Balhoff, Matthew T. (committee member), Delshad, Mojdeh (committee member), Arbogast, Todd J. (committee member).

Subjects/Keywords: Fractured carbonates; EOR; Vug connectivity; Core characterization; Wettability alteration; Anionic surfactant; Divalent ion scavengers; Spontaneous imbibition; Scaling; Tracer tests

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APA (6^th Edition):

Chen, P. (2014). Enhanced oil recovery in fractured vuggy carbonates. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31396

Chicago Manual of Style (16^th Edition):

Chen, Peila. “Enhanced oil recovery in fractured vuggy carbonates.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/31396.

MLA Handbook (7^th Edition):

Chen, Peila. “Enhanced oil recovery in fractured vuggy carbonates.” 2014. Web. 18 Jan 2021.

Vancouver:

Chen P. Enhanced oil recovery in fractured vuggy carbonates. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/31396.

Council of Science Editors:

Chen P. Enhanced oil recovery in fractured vuggy carbonates. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/31396

5. -1218-7450. Implicit boundary integral methods.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32830

► Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary… (more)

▼ Boundary integral methods (BIMs) solve constant coefficient, linear partial differential equations (PDEs) which have been formulated as integral equations. Implicit BIMs (IBIMs) transform these boundary integrals in a level set framework, where the boundaries are described implicitly as the zero level set of a Lipschitz function. The advantage of IBIMs is that they can work on a fixed Cartesian grid without having to parametrize the boundaries. This dissertation extends the IBIM model and develops algorithms for problems in two application areas. The first part of this dissertation considers nonlinear interface dynamics driven by bulk diffusion, which involves solving Dirichlet Laplace Problems for multiply connected regions and propagating the interface according to the solutions of the PDE at each time instant. We develop an algorithm that inherits the advantages of both level set methods (LSMs) and BIMs to simulate the nonlocal front propagation problem with possible topological changes. Simulation results in both 2D and 3D are provided to demonstrate the effectiveness of the algorithm. The second part considers wave scattering problems in unbounded domains. To obtain solutions at eigenfrequencies, boundary integral formulations use a combination of double and single layer potentials to cover the null space of the single layer integral operator. However, the double layer potential leads to a hypersingular integral in Neumann problems. Traditional schemes involve an interpretation of the integral as its Hadamard's Finite Part or a complicated process of element kernel regularization. In this thesis, we introduce an extrapolatory implicit boundary integral method (EIBIM) that evaluates the natural definition of the BIM. It is able to solve the Helmholtz problems at eigenfrequencies and requires no extra complication in different dimensions. We illustrate numerical results in both 2D and 3D for various boundary shapes, which are implicitly described by level set functions. Advisors/Committee Members: Tsai, Yen-Hsi R. (advisor), Arbogast, Todd (committee member), Biros, George (committee member), Engquist, Bjorn (committee member), Ren, Kui (committee member).

Subjects/Keywords: Boundary integral methods; Level set methods; Mullins-Sekerka; Helmholtz equation; Laplace equation; Multiply connected domain; Exterior problem; Differential equation

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APA (6^th Edition):

-1218-7450. (2015). Implicit boundary integral methods. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32830

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Chicago Manual of Style (16^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/32830.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1218-7450. “Implicit boundary integral methods.” 2015. Web. 18 Jan 2021.

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Author name may be incomplete

Vancouver:

-1218-7450. Implicit boundary integral methods. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/32830.

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Author name may be incomplete

Council of Science Editors:

-1218-7450. Implicit boundary integral methods. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32830

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

University of Texas – Austin

6. Zhao, Xikai. Implicit finite volume WENO schemes for solving hyperbolic conservation laws.

Degree: PhD, Mathematics, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/2982

► In this dissertation, we consider high order accurate, implicit, finite volume, weighted essentially non-oscillatoy (WENO) schemes for solving advection-diffusion equations. Our schemes are locally mass… (more)

Subjects/Keywords: Hyperbolic; WENO reconstruction; WENO-AO; Implicit time-stepping

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zhao, X. (2019). Implicit finite volume WENO schemes for solving hyperbolic conservation laws. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2982

Chicago Manual of Style (16^th Edition):

Zhao, Xikai. “Implicit finite volume WENO schemes for solving hyperbolic conservation laws.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://dx.doi.org/10.26153/tsw/2982.

MLA Handbook (7^th Edition):

Zhao, Xikai. “Implicit finite volume WENO schemes for solving hyperbolic conservation laws.” 2019. Web. 18 Jan 2021.

Vancouver:

Zhao X. Implicit finite volume WENO schemes for solving hyperbolic conservation laws. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Jan 18]. Available from: http://dx.doi.org/10.26153/tsw/2982.

Council of Science Editors:

Zhao X. Implicit finite volume WENO schemes for solving hyperbolic conservation laws. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/2982

University of Texas – Austin

7. -6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/2865

► Discontinuous Galerkin (DG) methods combine the advantages of classical finite element and finite volume methods. Like finite volume methods, through the use of discontinuous spaces… (more)

▼ Discontinuous Galerkin (DG) methods combine the advantages of classical finite element and finite volume methods. Like finite volume methods, through the use of discontinuous spaces in the discrete functional setting, we automatically have local conservation, an essential property for a numerical method to behave well when applied to hyperbolic conservation laws. Like classical finite element methods, DG methods allow for higher order approximations with compact stencils. For time-dependent problems with implicit time stepping and for steady-state problems, DG methods give a larger globally coupled linear system than continuous Galerkin methods (especially for three dimensional problems and low polynomial orders). The primary motivation of the hybridized (or hybridizable) discontinuous Galerkin (HDG) methods is to reduce the number of globally coupled unknowns in DG methods when implicit time stepping or direct-to-steady-state solutions are desired. This is accomplished by the introduction of new “trace unknowns” defined on the mesh skeleton, the definition of one-sided numerical fluxes, and the enforcement of local conservation. This results in a globally coupled linear system where the local “volume unknowns” can be eliminated in a Schur complement procedure, resulting in a reduced globally coupled system in terms of only the trace unknowns. Magnetohydrodynamics (MHD) is the study of the flow of electrically conducting fluids under the influence of magnetic fields. The MHD equations are used to describe important physical phenomena including laboratory plasmas (plasma confinement in fusion energy devices), astrophysical plasmas (solar coronas, planetary magnetospheres) and liquid metal flows (metallurgy processes, the Earth’s molten core, cooling for nuclear reactors). Incompressible MHD, which is the main focus of this work, is relevant in low Lundquist number liquid metals, in high Lundquist number, large guide field fusion plasmas, and in low Mach number compressible flows. The equations of MHD are highly nonlinear, and are characterized by physical phenomena spanning wide ranges of length and time scales. For numerical methods, this presents challenges in both spatial and temporal discretization. In terms of temporal discretization, fully implicit numerical methods are attractive in their robustness; they allow for stable, high-order time integration over long time scales of interest. Advisors/Committee Members: Bui-Thanh, Tan (advisor), Arbogast, Todd (committee member), Demkowicz, Leszek (committee member), Ghattas, Omar (committee member), Shadid, John (committee member), Waelbroeck, François (committee member).

Subjects/Keywords: Finite element methods; Discontinuous Galerkin methods; Hybridized discontinuous Galerkin methods; Stokes equations; Oseen equations; Magnetohydrodynamics; Resistive magnetohydrodynamics

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APA (6^th Edition):

-6327-2527. (2018). Hybridized discontinuous Galerkin methods for magnetohydrodynamics. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/2865

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Chicago Manual of Style (16^th Edition):

-6327-2527. “Hybridized discontinuous Galerkin methods for magnetohydrodynamics.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://dx.doi.org/10.26153/tsw/2865.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-6327-2527. “Hybridized discontinuous Galerkin methods for magnetohydrodynamics.” 2018. Web. 18 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Jan 18]. Available from: http://dx.doi.org/10.26153/tsw/2865.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-6327-2527. Hybridized discontinuous Galerkin methods for magnetohydrodynamics. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://dx.doi.org/10.26153/tsw/2865

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Author name may be incomplete

University of Texas – Austin

8. -8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/32535

► This dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to… (more)

▼ This dissertations focuses on solving the advection problem with the motivation of simulating transport in porous media. A quadrature based Eulerian-Lagrangian scheme is developed to solve the nonlinear advection problem in multiple spatial dimensions. The schemes combines the ideas of Lagrangian traceline methods with high order WENO reconstructions to compute the mass that flows into a given cell over a time step. These schemes are important since they have a relaxed CFL constraint, and can be run in parallel. In this thesis we provide two improvements to Eulerian-Lagrangian schemes. To do this an integration based WENO (IWENO) interpolation technique is derived by reconstructing the primitive function and differentiating. This technique gives a high order reconstruction of the mass at an arbitrary point. This WENO scheme is used to solve the linear advection problem. A scheme is derived by backwards tracing of quadrature points located on mesh elements. The mass at these tracepoints is used to compute the mass in the trace region, without resolving its boundary. This process defines a high order quadrature Eulerian-Lagrangian WENO (QEL-WENO) scheme that solves the multi-dimensional problem without the need for a spatial splitting technique. The second improvement is for solving the nonlinear advection problem using an approximate velocity field. The velocity field is used to transport mass in the manner of a standard Eulerian-Lagrangian scheme. Then a flux correction is applied to compute the flow across the tracelines. The contribution is to use a variation of the IWENO technique to reduce the stencil size of this computation. Numerical results are presented demonstrating the capabilities of the scheme. An application to two-phase flow in porous media is provided. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Balhoff, Matthew T (committee member), Chen, Thomas (committee member), Gonzalez, Oscar (committee member), Vasseur, Alexis F (committee member), Wheeler, Mary F (committee member).

Subjects/Keywords: Hyperbolic transport; Semi-Lagrangian; Finite volume; Characteristics; Traceline; WENO reconstruction; Compact stencil; Two-phase

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APA (6^th Edition):

-8477-1384. (2015). A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/32535

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Chicago Manual of Style (16^th Edition):

-8477-1384. “A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/32535.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-8477-1384. “A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation.” 2015. Web. 18 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/32535.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-8477-1384. A quadrature Eulerian-Lagrangian WENO scheme for reservoir simulation. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/32535

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

9. -4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows.

Degree: PhD, Engineering Mechanics, 2019, University of Texas – Austin

URL: http://dx.doi.org/10.26153/tsw/5476

► As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD)… (more)

▼ As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD) tools in aerospace and research facilities are widely used to evaluate the aerodynamic performance of aircraft or wings. Weather forecasts are highly dependent on numerical weather prediction (NWP) model. However, it is still difficult to simulate the complex physical phenomena of a wide range of length and time scales with modern computational resources. In this study, we develop a robust, efficient and high-order accurate numerical methods and techniques to tackle the challenges. First, we use high-order spatial discretization using (hybridized) discontinuous Galerkin (DG) methods. The DG method combines the advantages of finite volume and finite element methods. As such, it is well-suited to problems with large gradients including shocks and with complex geometries, and large-scale simulations. However, DG typically has many degrees-of-freedoms. To mitigate the expense, we use hybridized DG (HDG) method that introduces new “trace unknowns” on the mesh skeleton (mortar interfaces) to eliminate the local “volume unknowns” with static condensation procedure and reduces globally coupled system when implicit time-stepping is required. Also, since the information between the elements is exchanged through the mesh skeleton, the mortar interfaces can be used as a glue to couple multi-phase regions, e.g., solid and fluid regions, or non-matching grids, e.g., a rotating mesh and a stationary mesh. That is the HDG method provides an efficient and flexible coupling environment compared to standard DG methods. Second, we develop an HDG-DG IMEX scheme for an efficient time integrating scheme. The idea is to divide the governing equations into stiff and nonstiff parts, implicitly treat the former with HDG methods, and explicitly treat the latter with DG methods. The HDG-DG IMEX scheme facilitates high-order temporal and spatial solutions, avoiding too small a time step. Numerical results show that the HDG-DG IMEX scheme is comparable to an explicit Runge-Kutta DG scheme in terms of accuracy while allowing for much larger timestep sizes. We also numerically observe that IMEX HDG-DG scheme can be used as a tool to suppress the high-frequency modes such as acoustic waves or fast gravity waves in atmospheric or ocean models. In short, IMEX HDG-DG methods are attractive for applications in which a fast and stable solution is important while permitting inaccurate processing of the fast modes. Third, we also develop an EXPONENTIAL DG scheme for an efficient time integrators. Similar to the IMEX method, the governing equations are separated into linear and nonlinear parts, then the two parts are spatially discretized with DG methods. Next, we analytically integrate the linear term and approximate the nonlinear term with respect to time. This method accurately handles the fast wave modes in the linear operator. To efficiently evaluate a matrix exponential, we employ… Advisors/Committee Members: Bui-Thanh, Tan (advisor), Bisetti, Fabrizio (committee member), Willcox, Karen E (committee member), Demkowicz, Leszek F (committee member), Ghattas, Omar (committee member), Arbogast, Todd (committee member).

Subjects/Keywords: Discontinuous Galerkin; DG; HDG; Hybridized DG; IMEX; Implicit-explicit; Exponential time integrator; ALE; Arbitrary Lagrangian-Eulerian; Sliding mesh; Nonconforming mesh; Degenerate elliptic equation; Mortar; Scalability

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APA (6^th Edition):

-4649-9727. (2019). High-order (hybridized) discontinuous Galerkin method for geophysical flows. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://dx.doi.org/10.26153/tsw/5476

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Chicago Manual of Style (16^th Edition):

-4649-9727. “High-order (hybridized) discontinuous Galerkin method for geophysical flows.” 2019. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://dx.doi.org/10.26153/tsw/5476.

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MLA Handbook (7^th Edition):

-4649-9727. “High-order (hybridized) discontinuous Galerkin method for geophysical flows.” 2019. Web. 18 Jan 2021.

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Author name may be incomplete

Vancouver:

-4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2019. [cited 2021 Jan 18]. Available from: http://dx.doi.org/10.26153/tsw/5476.

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Author name may be incomplete

Council of Science Editors:

-4649-9727. High-order (hybridized) discontinuous Galerkin method for geophysical flows. [Doctoral Dissertation]. University of Texas – Austin; 2019. Available from: http://dx.doi.org/10.26153/tsw/5476

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

10. Voelkel, Stephen Joseph. Thermal nonequilibrium models for high-temperature reactive processes.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/47234

► This dissertation examines how thermal nonequilibrium affects mixing and combustion in high-enthalpy, high-speed systems such as reentry vehicles, scramjets, and detonation-driven engines. Specifically, the focus… (more)

▼ This dissertation examines how thermal nonequilibrium affects mixing and combustion in high-enthalpy, high-speed systems such as reentry vehicles, scramjets, and detonation-driven engines. Specifically, the focus is in the development of physical models that accurately describe thermal nonequilibrium in a continuum-scale ow and its relative effect on mixing and reaction processes. To this end, the quasi-classical trajectory method is utilized, in which bimolecular collisions (or trajectories) are individually simulated. The aggregate of the outcomes from many trajectories is then used to calculate the macroscopic reaction and scattering rates of the system. A QCT program is presented for massively parallel simulations, which includes an algorithm for calculating and tabulating the potential energy surface throughout the QCT simulation. Using the QCT program, chain-reactions in hydrogen combustions are simulated, and the subsequent rates are used directly in CFD simulations as well as to develop vibrational nonequilibrium reaction rate models. Also, nitrogen dissociation is simulated to calculate the dissociation rate as a function of independent translational, rotational, and vibrational temperatures, thus extending the conventional two-temperature model. This simulation is made tractable via a new method for selectively sampling trajectories. Finally, the QCT program is utilized to calculate N₂-O₂ inelastic cross-sections. This work was motivated by CFD simulations of experimental observations which indicated that the conventional N₂-O₂ vibrational exchange rates were invalid at moderate temperatures. The QCT-calculated rates support these observations. In addition to QCT-based simulations, 1D and 2D simulations of detonation waves with vibrational nonequilibrium (modeled using the aforementioned data) are analyzed. It is observed that nonequilibrium only marginally affects the induction zone of the detonation wave. However, in the 2D simulations, it is observed that vibrational nonequilibrium plays a critical role in determining detonation cell sizes. In summary, vibrational nonequilibrium is analyzed using QCT for a variety of systems, and the resulting data is utilized to develop CFD-scale models. We have high confidence in the resulting models because they are derived from first principles and microscopic observations as opposed to simplified models or empirical fits. Advisors/Committee Members: Varghese, Philip L. (advisor), Raman, Venkat (advisor), Arbogast, Todd J (committee member), Dawson, Clint N (committee member), Moser, Robert D (committee member), Stanton, John F (committee member).

Subjects/Keywords: Thermal nonequilibrium; Scramjet; Reentry vehicle; Quasi-classical trajectory; QCT; Hydrogen combustion; Nitrogen dissociation; Nitrogen-oxygen scattering

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APA (6^th Edition):

Voelkel, S. J. (2016). Thermal nonequilibrium models for high-temperature reactive processes. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/47234

Chicago Manual of Style (16^th Edition):

Voelkel, Stephen Joseph. “Thermal nonequilibrium models for high-temperature reactive processes.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/47234.

MLA Handbook (7^th Edition):

Voelkel, Stephen Joseph. “Thermal nonequilibrium models for high-temperature reactive processes.” 2016. Web. 18 Jan 2021.

Vancouver:

Voelkel SJ. Thermal nonequilibrium models for high-temperature reactive processes. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/47234.

Council of Science Editors:

Voelkel SJ. Thermal nonequilibrium models for high-temperature reactive processes. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/47234

University of Texas – Austin

11. Mohammad Reza Beygi, Mohammad Reza. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.

Degree: PhD, Petroleum engineering, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/45556

► Enhanced oil recovery (EOR) techniques have the potential to improve hydrocarbon recovery and project economics substantially. Characterizing fluid displacement and the relevant multiphase flow properties… (more)

▼ Enhanced oil recovery (EOR) techniques have the potential to improve hydrocarbon recovery and project economics substantially. Characterizing fluid displacement and the relevant multiphase flow properties are essential to modeling EOR processes to reliably forecast the performance and economics. The spatial-temporal distribution of fluids spans a broad spectrum of composition and saturation spaces. In addition, a fundamental understanding of characteristic parameters of interphase mass-transfer in various EOR applications is crucial to capture and model fluid displacement. Relative permeability is a critical characteristic petrophysical property for modeling fluid displacement in porous media. Also, hysteresis phenomena govern physics of fluid flow in many subsurface applications such as multicyclic EOR processes, geological CO2 sequestration, and natural gas storage. Capillary trapping is the essence of hysteresis to trap fluids. In this research, we developed a high-fidelity computational tool for integrating compositional three-phase relative permeability and hysteresis to assist in accurate modeling of multicycle and compositional EOR methods. This viable tool can be implemented into general-purpose reservoir simulators to model field-scale projects. It consists of an integrated compositionally-consistent three-phase relative permeability and three-phase hysteresis models. The developed three-phase relative permeability model is valid on entire saturation and composition spaces, is simple with one free parameter for each phase, and is versatile for all phases and wettability states. The general model is saturation-path dependent and adopts a linear saturation-weighted interpolation scheme for calculation of relative permeability parameters. For the compositional relative permeability modeling, we developed a general framework applicable to hydrocarbon and non-hydrocarbon phases. The developed framework provides a pragmatic approach for adding the direct impact of composition, pressure, and temperature and is independent of the conventional phase-labeling method. The proposed framework unifies thermodynamics, petrophysics, and geochemistry to enhanced relative permeability modeling. Relative permeability parameters are calculated based on a mapping scheme of current-state bulk and interphase Gibbs free energy onto corresponding initial-state values. We applied the developed framework to modeling lowsalinity waterflood and complex fluid displacement of near-critical fluids. The three-phase hysteresis model provides a general and straightforward approach for calculation of capillary trapping in multicyclic processes. The developed hysteresis model provides a set of cycle-dependent relative permeability curves and applies to any three-phase relative permeability model by incorporating the free-saturation concept. We implemented the developed toolbox into two in-house compositional reservoir simulators (i.e., IPARS and UT-DOECO2). Several synthetic field cases are discussed to validate the implemented models… Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor), Pope, Gary A (committee member), Sepehrnoori, Kamy (committee member), Mohanty, Kishory K. (committee member), Arbogast, Todd (committee member).

Subjects/Keywords: Three-phase; Relative permeability; Hysteresis; Aqueous; Near-critical fluid; Low-tension gas flood; Gibbs free energy; Foam; EOR; Electrolyte

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APA (6^th Edition):

Mohammad Reza Beygi, M. R. (2016). Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/45556

Chicago Manual of Style (16^th Edition):

Mohammad Reza Beygi, Mohammad Reza. “Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/45556.

MLA Handbook (7^th Edition):

Mohammad Reza Beygi, Mohammad Reza. “Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes.” 2016. Web. 18 Jan 2021.

Vancouver:

Mohammad Reza Beygi MR. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/45556.

Council of Science Editors:

Mohammad Reza Beygi MR. Development of compositional three-phase relative permeability and hysteresis models and their application to EOR processes. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/45556

12. -5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2016, University of Texas – Austin

URL: http://hdl.handle.net/2152/46503

► The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability,… (more)

▼ The coupling between subsurface flow and reservoir geomechanics plays a critical role in obtaining accurate results for models involving reservoir deformation, surface subsidence, well stability, sand production, waste deposition, hydraulic fracturing, CO₂ sequestration, and hydrocarbon recovery. From a pure computational point of view, such a coupling can be quite a challenging and complicated task. This stems from the fact that the constitutive equations governing geomechanical deformations are different in nature from those governing porous media flow. The geomechanical effects account for the influence of deformations in the porous media caused due to the pore pressure and can be very important especially in the case of stress-sensitive and fractured reservoirs. Considering that fractures are very much prevalent in the porous media and they have strong influence on the flow profiles, it is important to study coupled geomechanics and flow problems in fractured reservoirs. In this work, we pursue three main objectives: first, to rigorously design and analyze iterative and explicit coupling algorithms for coupling flow and geomechanics in both poro-elasitc and fractured poro-elastic reservoirs. The analysis of iterative coupling schemes relies on studying the equations satisfied by the difference of iterates and using a Banach contraction argument to derive geometric convergence (Banach fixed-point contraction) results. The analysis of explicit coupling schemes result in analogous stability estimates. In this work, conformal Galerkin is used for mechanics, and a mixed formulation, including the Multipoint Flux Mixed Finite Element method as a special case, is used for the flow model. For fractured poro-elastic media, our iteratively coupled schemes are adaptations, due to the presence of fractures, of the classical fixed stress-splitting scheme, in which fractures are treated as possibly non-planar interfaces. The second main objective in this work is to exploit the different time scales of the mechanics and flow problems. Due to its physical nature, the geomechanics problem can cope with a coarser time step compared to the flow problem. This makes the multirate coupling scheme, the one in which the flow problem takes several (finer) time steps within the same coarse mechanics time step, a natural candidate in this setting. Inspired by that, we rigorously formulate and analyze convergence properties of both multirate iterative and explicit coupling schemes in both poro-elastic and fractured poro-elastic reservoirs. In addition, our theoretically derived Banach contraction estimates are validated against numerical simulations. The third objective in this work is to optimize the solution strategy of the nonlinear flow model in coupled flow and mechanics schemes. The global inexact Newton method, combined with the line search backtracking algorithm along with heuristic forcing functions, can be efficiently employed to reduce the number of flow linear iterations, and hence, the overall CPU run time. We first validate… Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Demkowicz, Leszek F. (committee member), Delshad, Mojdeh (committee member), Dhillon, Inderjit (committee member), Kumar, Kundan (committee member).

Subjects/Keywords: Poroelasticity; Biot system; Fixed-stress split iterative coupling; Undrained split iterative coupling; Explicit coupling; Single rate scheme; Multirate scheme; Banach fixed-point contraction; Fractured poroelastic media; A priori error estiamtes; Global inexact Newton methods

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APA (6^th Edition):

-5603-2533. (2016). Efficient algorithms for flow models coupled with geomechanics for porous media applications. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46503

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Chicago Manual of Style (16^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/46503.

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Author name may be incomplete

MLA Handbook (7^th Edition):

-5603-2533. “Efficient algorithms for flow models coupled with geomechanics for porous media applications.” 2016. Web. 18 Jan 2021.

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Author name may be incomplete

Vancouver:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/46503.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5603-2533. Efficient algorithms for flow models coupled with geomechanics for porous media applications. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/46503

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Author name may be incomplete

University of Texas – Austin

13. -3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin

URL: http://hdl.handle.net/2152/68968

► Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂… (more)

▼ Multiscale modeling of subsurface flow and transport is a major area of interest in several applications including petroleum recovery evaluations, nuclear waste disposal systems, CO₂ sequestration, groundwater remediation and contaminant plume migration in heterogeneous porous media. During these processes the direct numerical simulation is computationally intensive due to detailed fine scale characterization of the subsurface formations. The main objective of this work is to develop an efficient multiscale framework to reduce usage of fine scale properties associated with advection and diffusion/dispersion, while maintaining accuracy of quantities of interest including mass balance, pressure, velocity, concentration. Another purpose of this work is to investigate the adaptivity criteria in transport and flow problems numerically and/or theoretically based on error estimates. We propose a new adaptive numerical homogenization method using numerical homogenization and Enhanced Velocity Mixed Finite Element Method (EVMFEM). We focus on upscaling the permeability and porosity fields for slightly (nonlinear) compressible single phase Darcy flow and transport problems in heterogeneous porous media. The fine grids are used in the transient regions where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [85]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this dissertation, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium. We have also derived a priori error estimate for a parabolic problem using Backward Euler and Crank-Nicolson method in time and EVMFEM in space. Next, we have established a posteriori error estimate in EVMFEM setting for incompressible flow problems. We first propose the flux reconstruction for error estimates and prove the upper and lower bound theorems. Next, the explicit residual-based estimates and the recovery-based error estimates with the post-processed pressure are derived theoretically. Numerical experiments are conducted to show that the proposed estimators are effective indicators of local error for incompressible flow problems. Advisors/Committee Members: Wheeler, Mary F. (Mary Fanett) (advisor), Arbogast, Todd (committee member), Balhoff, Matthew (committee member), Tsai, Yen-Hsi Richard (committee member), Wildey, Tim (committee member).

Subjects/Keywords: Enhanced velocity; Numerical homogenization; Adaptive mesh refinement; Multiscale methods; Error estimates; A posteriori error; A priori error; SPE10 dataset

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APA (6^th Edition):

-3958-8871. (2018). A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68968

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Chicago Manual of Style (16^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/68968.

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MLA Handbook (7^th Edition):

-3958-8871. “A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme.” 2018. Web. 18 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/68968.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-3958-8871. A new adaptive modeling of flow and transport in porous media using an enhanced velocity scheme. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/68968

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University of Texas – Austin

14. -5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/68171

► Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work,… (more)

▼ Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements. Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Wheeler, Mary F (committee member), Ghattas, Omar (committee member), Demkowicz, Leszek F (committee member), Hesse, Marc A (committee member).

Subjects/Keywords: Multiphase flow; Porous media; Mixed finite element; H(div)-approximation; Arbogast-Tao element; Arbogast-Correa element; Direct serendipity element; Serendipity element; Enriched Galerkin method; Entropy viscosity stabilization; Capillary flux reconstruction; Heterogeneous capillary pressure; Two-phase flow

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APA (6^th Edition):

-5063-5889. (2017). Numerical analysis of multiphase flows in porous media on non-rectangular geometry. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/68171

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Chicago Manual of Style (16^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5063-5889. “Numerical analysis of multiphase flows in porous media on non-rectangular geometry.” 2017. Web. 18 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/68171.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5063-5889. Numerical analysis of multiphase flows in porous media on non-rectangular geometry. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/68171

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15. San Martin Gomez, Mario, 1968-. A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media.

Degree: PhD, Mathematics, 2007, University of Texas – Austin

URL: http://hdl.handle.net/2152/13131

► A vuggy porous medium is one with many small cavities called vugs, which are interconnected in complex ways forming channels that can support high flow… (more)

Subjects/Keywords: Porous materials – Mathematical models; Multigrid methods (Numerical analysis); Finite element method; Fluid dynamics – Mathematical models; Darcy's law; Stokes equations

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APA (6^th Edition):

San Martin Gomez, Mario, 1. (2007). A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/13131

Chicago Manual of Style (16^th Edition):

San Martin Gomez, Mario, 1968-. “A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media.” 2007. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/13131.

MLA Handbook (7^th Edition):

San Martin Gomez, Mario, 1968-. “A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media.” 2007. Web. 18 Jan 2021.

Vancouver:

San Martin Gomez, Mario 1. A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2007. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/13131.

Council of Science Editors:

San Martin Gomez, Mario 1. A three dimensional finite element method and multigrid solver for a Darcy-Stokes system and applications to vuggy porous media. [Doctoral Dissertation]. University of Texas – Austin; 2007. Available from: http://hdl.handle.net/2152/13131

16. Wang, Xingyao, active 21st century. Krylov methods for solving linear systems.

Degree: MSin Computational Science, Engineering, and Mathematics, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/62387

► Krylov methods are considered as one of the most popular classes of numerical methods to solve large sparse linear systems of equations. One of the… (more)

Subjects/Keywords: Krylov methods; Linear systems; Conjugate gradient algorithm; GMRES algorithm; Preconditions

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APA (6^th Edition):

Wang, Xingyao, a. 2. c. (2017). Krylov methods for solving linear systems. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/62387

Chicago Manual of Style (16^th Edition):

Wang, Xingyao, active 21st century. “Krylov methods for solving linear systems.” 2017. Masters Thesis, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/62387.

MLA Handbook (7^th Edition):

Wang, Xingyao, active 21st century. “Krylov methods for solving linear systems.” 2017. Web. 18 Jan 2021.

Vancouver:

Wang, Xingyao a2c. Krylov methods for solving linear systems. [Internet] [Masters thesis]. University of Texas – Austin; 2017. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/62387.

Council of Science Editors:

Wang, Xingyao a2c. Krylov methods for solving linear systems. [Masters Thesis]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/62387

17. Taicher, Abraham Levy. Mixed framework for Darcy-Stokes mixtures.

Degree: PhD, Computational and Applied Mathematics, 2014, University of Texas – Austin

URL: http://hdl.handle.net/2152/28357

► We consider the system of equations arising from mantle dynamics introduced by McKenzie (J. Petrology, 1985). In this multi-phase model, the fluid melt velocity obeys… (more)

▼ We consider the system of equations arising from mantle dynamics introduced by McKenzie (J. Petrology, 1985). In this multi-phase model, the fluid melt velocity obeys Darcy's law while the deformable "solid" matrix is governed by a highly viscous Stokes equation. The system is then coupled through mass conservation and compaction relations. Together these equations form a coupled Darcy-Stokes system on a continuous single-domain mixture of fluid and matrix. The porosity φ, representing the relative volume of fluid melt to the bulk volume, is assumed to be much smaller than one. When coupled with solute transport and thermal evolution in a time-dependent problem, the model transitions dynamically from a non-porous single phase solid to a two-phase porous medium. Such mixture models have an advantage for numerical approximation since the free boundary between the one and two-phase regions need not be determined explicitly. The equations of mantle dynamics apply to a wide range of applications in deep earth physics such as mid-ocean ridges, subduction zones, and hot-spot volcanism, as well as to glacier dynamics and other two-phase flows in porous media. Mid-ocean ridges form when viscous corner flow of the solid mantle focuses fluid toward a central ridge. Melt is believed to migrate upward until it reaches the lithospheric "tent" where it then moves toward the ridge in a high porosity band. Simulation of this physical phenomenon required confidence in numerical methods to handle highly heterogeneous porosity as well as the single-phase to two-phase transition. In this work we present a standard mixed finite element method for the equations of mantle dynamics and investigate its limitations for vanishing porosity. While stable and optimally convergent for porosity bounded away from zero, the stability estimates we obtain suggest, and numerical results show, the method becomes unstable as porosity approaches zero. Moreover, the fluid pressure is no longer a physical variable when the fluid phase disappears and thus is not a good variable for numerical methods. Inspired by the stability estimates of the standard method, we develop a novel stable mixed method with uniqueness and existence of solutions by studying a linear degenerate elliptic sub-problem akin to the Darcy part of the full model: [mathematical equation], where a and b satisfy a(0)=b(0)=0 and are otherwise positive, and the porosity φ ≥ 0 may be zero on a set of positive measure. Using scaled variables and mild assumptions on the regularity of φ, we develop a practical mass-conservative method based on lowest order Raviart-Thomas finite elements. Finally, we adapt the numerical method for the sub-problem to the full system of equations. We show optimal convergence for sufficiently smooth solutions for a compacting column and mid-ocean ridge-like corner flow examples, and investigate accuracy and stability for less regular problems Advisors/Committee Members: Arbogast, Todd James, 1957- (advisor), Hesse, Marc (advisor).

Subjects/Keywords: Degenerate elliptic; Mixture theory; Energy bounds; Mantle dynamics; Mixed method

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APA (6^th Edition):

Taicher, A. L. (2014). Mixed framework for Darcy-Stokes mixtures. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/28357

Chicago Manual of Style (16^th Edition):

Taicher, Abraham Levy. “Mixed framework for Darcy-Stokes mixtures.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/28357.

MLA Handbook (7^th Edition):

Taicher, Abraham Levy. “Mixed framework for Darcy-Stokes mixtures.” 2014. Web. 18 Jan 2021.

Vancouver:

Taicher AL. Mixed framework for Darcy-Stokes mixtures. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/28357.

Council of Science Editors:

Taicher AL. Mixed framework for Darcy-Stokes mixtures. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/28357

18. Ringer, Nathanael David. Three essays on valuation and investment in incomplete markets.

Degree: PhD, Mathematics, 2011, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2011-05-2816

► Incomplete markets provide many challenges for both investment decisions and valuation problems. While both problems have received extensive attention in complete markets, there remain many… (more)

▼ Incomplete markets provide many challenges for both investment decisions and valuation problems. While both problems have received extensive attention in complete markets, there remain many open areas in the theory of incomplete markets. We present the results in three parts. In the first essay we consider the Merton investment problem of optimal portfolio choice when the traded instruments are the set of zero-coupon bonds. Working within a Markovian Heath-Jarrow-Morton framework of the interest rate term structure driven by an infinite dimensional Wiener process, we give sufficient conditions for the existence and uniqueness of an optimal investment strategy. When there is uniqueness, we provide a characterization of the optimal portfolio. Furthermore, we show that a specific Gauss-Markov random field model can be treated within this framework, and explicitly calculate the optimal portfolio. We show that the optimal portfolio in this case can be identified with the discontinuities of a certain function of the market parameters. In the second essay we price a claim, using the indifference valuation methodology, in the model presented in the first section. We appeal to the indifference pricing framework instead of the classic Black-Scholes method due to the natural incompleteness in such a market model. Because we price time-sensitive interest rate claims, the units in which we price are very important. This will require us to take care in formulating the investor’s utility function in terms of the units in which we express the wealth function. This leads to new results, namely a general change-of-numeraire theorem in incomplete markets via indifference pricing. Lastly, in the third essay, we propose a method to price credit derivatives, namely collateralized debt obligations (CDOs) using indifference. We develop a numerical algorithm for pricing such CDOs. The high illiquidity of the CDO market coupled with the allowance of default in the underlying traded assets creates a very incomplete market. We explain the market-observed prices of such credit derivatives via the risk aversion of investors. In addition to a general algorithm, several approximation schemes are proposed. Advisors/Committee Members: Zariphopoulou, Thaleia, 1962- (advisor), Arbogast, Todd (committee member), Gamba, Irene (committee member), Tompaidis, Stathis (committee member), Zitkovic, Gordan (committee member).

Subjects/Keywords: Credit default; Indifference pricing; Infinite-dimensional stochastic processes; Malliavin calculus; Numeraire; Utility maximization; Incomplete markets; Credit derivatives; Collateralized debt obligations; Optimal investment; Pricing

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APA (6^th Edition):

Ringer, N. D. (2011). Three essays on valuation and investment in incomplete markets. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2011-05-2816

Chicago Manual of Style (16^th Edition):

Ringer, Nathanael David. “Three essays on valuation and investment in incomplete markets.” 2011. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2011-05-2816.

MLA Handbook (7^th Edition):

Ringer, Nathanael David. “Three essays on valuation and investment in incomplete markets.” 2011. Web. 18 Jan 2021.

Vancouver:

Ringer ND. Three essays on valuation and investment in incomplete markets. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2011. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2011-05-2816.

Council of Science Editors:

Ringer ND. Three essays on valuation and investment in incomplete markets. [Doctoral Dissertation]. University of Texas – Austin; 2011. Available from: http://hdl.handle.net/2152/ETD-UT-2011-05-2816

19. Sun, Tie, Ph. D. Upscaling and multiscale simulation by bridging pore scale and continuum scale models.

Degree: PhD, Petroleum Engineering, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-08-6119

► Many engineering and scientific applications of flow in porous media are characterized by transport phenomena at multiple spatial scales, including pollutant transport, groundwater remediation, and… (more)

▼ Many engineering and scientific applications of flow in porous media are characterized by transport phenomena at multiple spatial scales, including pollutant transport, groundwater remediation, and acid injection to enhance well production. Carbon sequestration in particular is a multiscale problem, because the trapping and leakage mechanisms of CO2 in the subsurface occur from the sub-pore level to the basin scale. Quantitative and predictive pore-scale modeling has long shown to be a valuable tool for studying fluid-rock interactions in porous media. However, due to the size limitation of the pore-scale models (10-4-10-2m), it is impossible to model an entire reservoir at the pore scale. A straightforward multiscale approach would be to upscale macroscopic parameters (e.g. permeability) directly from pore-scale models and then input them into a continuum-scale simulator. However, it has been found that the large-scale models do not predict in many cases. One possible reason for the inaccuracies is oversimplified boundary conditions used in this direct upscaling approach. The hypothesis of this work is that pore-level flow and upscaled macroscopic parameters depends on surrounding flow behavior manifested in the form of boundary conditions. The detailed heterogeneity captured by the pore-scale models may be partially lost if oversimplified boundary conditions are employed in a direct upscaling approach. As a result, extracted macroscopic properties may be inaccurate. Coupling the model to surrounding media (using finite element mortars to ensure continuity between subdomains) would result in more realistic boundary conditions, and can thus improve the accuracy of the upscaled parameters. To test the hypothesis, mortar coupling is employed to couple pore-scale models and also couple pore-scale models to continuum models. Flow field derived from mortar coupling and direct upscaling are compared, preferably against a true solution if one exists. It is found in this dissertation that pore-scale flow and upscaled parameters can be significantly affected by the surrounding media. Therefore, using arbitrary boundary conditions such as constant pressure and no-flow boundaries may yield misleading results. Mortar coupling captures the detailed variation on the interface and imposes realistic boundary conditions, thus estimating more accurate upscaled values and flow fields. An advanced upscaling tool, a Super Permeability Tensor (SPT) is developed that contains pore-scale heterogeneity in greater detail than a conventional permeability tensor. Furthermore, a multiscale simulator is developed taking advantage of mortar coupling to substitute continuum grids directly with pore-scale models where needed. The findings from this dissertation can significantly benefit the understanding of fluid flow in porous media, and, in particular, CO2 storage in geological formations which requires accurate modeling across multiple scales. The fine-scale models are sensitive to the boundary conditions, and the large scale modeling of… Advisors/Committee Members: Balhoff, Matthew T. (advisor), DiCarlo, David (committee member), Arbogast, Todd (committee member), Lake, Larry (committee member), Wheeler, Mary (committee member).

Subjects/Keywords: Reservoir simulation; Pore-scale simulation; Upscaling; Multiscale simulation; Mortar coupling; Network model

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APA (6^th Edition):

Sun, Tie, P. D. (2012). Upscaling and multiscale simulation by bridging pore scale and continuum scale models. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-6119

Chicago Manual of Style (16^th Edition):

Sun, Tie, Ph D. “Upscaling and multiscale simulation by bridging pore scale and continuum scale models.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2012-08-6119.

MLA Handbook (7^th Edition):

Sun, Tie, Ph D. “Upscaling and multiscale simulation by bridging pore scale and continuum scale models.” 2012. Web. 18 Jan 2021.

Vancouver:

Sun, Tie PD. Upscaling and multiscale simulation by bridging pore scale and continuum scale models. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6119.

Council of Science Editors:

Sun, Tie PD. Upscaling and multiscale simulation by bridging pore scale and continuum scale models. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-6119

University of Texas – Austin

20. Lehr, Heather Lyn. Analysis of a Darcy-Stokes system modeling flow through vuggy porous media.

Degree: PhD, Mathematics, 2004, University of Texas – Austin

URL: http://hdl.handle.net/2152/1234

► Our goal is to accurately model flow through subsurface systems composed of vuggy porous media. A vug is a small cavity in a porous medium… (more)

Subjects/Keywords: Porous materials – Mathematical models; Fluid dynamics – Mathematical models; Darcy's law; Stokes equations

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APA (6^th Edition):

Lehr, H. L. (2004). Analysis of a Darcy-Stokes system modeling flow through vuggy porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/1234

Chicago Manual of Style (16^th Edition):

Lehr, Heather Lyn. “Analysis of a Darcy-Stokes system modeling flow through vuggy porous media.” 2004. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/1234.

MLA Handbook (7^th Edition):

Lehr, Heather Lyn. “Analysis of a Darcy-Stokes system modeling flow through vuggy porous media.” 2004. Web. 18 Jan 2021.

Vancouver:

Lehr HL. Analysis of a Darcy-Stokes system modeling flow through vuggy porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2004. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/1234.

Council of Science Editors:

Lehr HL. Analysis of a Darcy-Stokes system modeling flow through vuggy porous media. [Doctoral Dissertation]. University of Texas – Austin; 2004. Available from: http://hdl.handle.net/2152/1234

University of Texas – Austin

21. Wang, Wenhao. An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems.

Degree: PhD, Computational and Applied Mathematics, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/7589

► A basic phenomenon modeled computationally is tracer transport in a flow field, such as in porous medium simulation. We analyze the stability and convergence of… (more)

Subjects/Keywords: Volume corrected characteristics-mixed method; Tracer transport problems

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APA (6^th Edition):

Wang, W. (2009). An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/7589

Chicago Manual of Style (16^th Edition):

Wang, Wenhao. “An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems.” 2009. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/7589.

MLA Handbook (7^th Edition):

Wang, Wenhao. “An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems.” 2009. Web. 18 Jan 2021.

Vancouver:

Wang W. An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2009. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/7589.

Council of Science Editors:

Wang W. An algorithm of a fully conservative volume corrected characteristics-mixed method for transport problems. [Doctoral Dissertation]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/7589

University of Texas – Austin

22. Rath, James Michael, 1975-. Multiscale basis optimization for Darcy flow.

Degree: PhD, Computational and Applied Mathematics, 2007, University of Texas – Austin

URL: http://hdl.handle.net/2152/3977

► Simulation of flow through a heterogeneous porous medium with fine-scale features can be computationally expensive if the flow is fully resolved. Coarsening the problem gives… (more)

Subjects/Keywords: Differential equations, Elliptic – Numerical solutions; Nonlinear theories; Darcy's law; Algorithms

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APA (6^th Edition):

Rath, James Michael, 1. (2007). Multiscale basis optimization for Darcy flow. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/3977

Chicago Manual of Style (16^th Edition):

Rath, James Michael, 1975-. “Multiscale basis optimization for Darcy flow.” 2007. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/3977.

MLA Handbook (7^th Edition):

Rath, James Michael, 1975-. “Multiscale basis optimization for Darcy flow.” 2007. Web. 18 Jan 2021.

Vancouver:

Rath, James Michael 1. Multiscale basis optimization for Darcy flow. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2007. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/3977.

Council of Science Editors:

Rath, James Michael 1. Multiscale basis optimization for Darcy flow. [Doctoral Dissertation]. University of Texas – Austin; 2007. Available from: http://hdl.handle.net/2152/3977

University of Texas – Austin

23. Brunson, Dana Sue. Simulating fluid flow in vuggy porous media.

Degree: PhD, Mathematics, 2005, University of Texas – Austin

URL: http://hdl.handle.net/2152/1832

► We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs.… (more)

Subjects/Keywords: Porous materials – Mathematical models; Fluid dynamics – Mathematical models; Finite element method

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APA (6^th Edition):

Brunson, D. S. (2005). Simulating fluid flow in vuggy porous media. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/1832

Chicago Manual of Style (16^th Edition):

Brunson, Dana Sue. “Simulating fluid flow in vuggy porous media.” 2005. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/1832.

MLA Handbook (7^th Edition):

Brunson, Dana Sue. “Simulating fluid flow in vuggy porous media.” 2005. Web. 18 Jan 2021.

Vancouver:

Brunson DS. Simulating fluid flow in vuggy porous media. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2005. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/1832.

Council of Science Editors:

Brunson DS. Simulating fluid flow in vuggy porous media. [Doctoral Dissertation]. University of Texas – Austin; 2005. Available from: http://hdl.handle.net/2152/1832

24. -2628-3585. Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling.

Degree: PhD, Computational and applied mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/31372

► Projecting the ice sheets' contribution to sea-level rise is difficult because of the complexity of accurately modeling ice sheet dynamics for the full polar ice… (more)

▼ Projecting the ice sheets' contribution to sea-level rise is difficult because of the complexity of accurately modeling ice sheet dynamics for the full polar ice sheets, because of the uncertainty in key, unobservable parameters governing those dynamics, and because quantifying the uncertainty in projections is necessary when determining the confidence to place in them. This work presents the formulation and solution of the Bayesian inverse problem of inferring, from observations, a probability distribution for the basal sliding parameter field beneath the Antarctic ice sheet. The basal sliding parameter is used within a high-fidelity nonlinear Stokes model of ice sheet dynamics. This model maps the parameters "forward" onto a velocity field that is compared against observations. Due to the continental-scale of the model, both the parameter field and the state variables of the forward problem have a large number of degrees of freedom: we consider discretizations in which the parameter has more than 1 million degrees of freedom. The Bayesian inverse problem is thus to characterize an implicitly defined distribution in a high-dimensional space. This is a computationally demanding problem that requires scalable and efficient numerical methods be used throughout: in discretizing the forward model; in solving the resulting nonlinear equations; in solving the Bayesian inverse problem; and in propagating the uncertainty encoded in the posterior distribution of the inverse problem forward onto important quantities of interest. To address discretization, a hybrid parallel adaptive mesh refinement format is designed and implemented for ice sheets that is suited to the large width-to-height aspect ratios of the polar ice sheets. An efficient solver for the nonlinear Stokes equations is designed for high-order, stable, mixed finite-element discretizations on these adaptively refined meshes. A Gaussian approximation of the posterior distribution of parameters is defined, whose mean and covariance can be efficiently and scalably computed using adjoint-based methods from PDE-constrained optimization. Using a low-rank approximation of the covariance of this distribution, the covariance of the parameter is pushed forward onto quantities of interest. Advisors/Committee Members: Ghattas, Omar N. (advisor), Stadler, Georg, Ph. D. (advisor), Arbogast, Todd (committee member), Biros, George (committee member), Catania, Ginny (committee member), Oden, John Tinsley (committee member).

Subjects/Keywords: Ice sheets; Parameter estimation; PDE-constrained optimization; Bayesian inversion; Adaptive mesh refinement; Quadtrees/octrees; Algebraic multigrid; Randomized methods

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APA (6^th Edition):

-2628-3585. (2015). Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31372

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-2628-3585. “Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/31372.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-2628-3585. “Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling.” 2015. Web. 18 Jan 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-2628-3585. Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/31372.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-2628-3585. Scalable, adaptive methods for forward and inverse problems in continental-scale ice sheet modeling. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31372

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

25. Gatto, Paolo, Ph. D. Modeling bone conduction of sound in the human head using hp-finite elements.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/19517

► This work focuses on the development of a reliable numerical model for investigating the bone-conduction of sound in the human head. The main challenge of… (more)

Subjects/Keywords: hp-finite elements; Bone conduction; Acoustics coupled with elasticity

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APA (6^th Edition):

Gatto, Paolo, P. D. (2012). Modeling bone conduction of sound in the human head using hp-finite elements. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/19517

Chicago Manual of Style (16^th Edition):

Gatto, Paolo, Ph D. “Modeling bone conduction of sound in the human head using hp-finite elements.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/19517.

MLA Handbook (7^th Edition):

Gatto, Paolo, Ph D. “Modeling bone conduction of sound in the human head using hp-finite elements.” 2012. Web. 18 Jan 2021.

Vancouver:

Gatto, Paolo PD. Modeling bone conduction of sound in the human head using hp-finite elements. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/19517.

Council of Science Editors:

Gatto, Paolo PD. Modeling bone conduction of sound in the human head using hp-finite elements. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/19517

26. Yuan, Changli. Commercial scale simulations of surfactant/polymer flooding.

Degree: PhD, Petroleum Engineering, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-08-401

► The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological… (more)

▼ The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological heterogeneity, unfavorable mobility ratio, and capillary forces, conventional oil recovery (including water flooding) leaves behind much oil in reservoir, often as much as 70% OOIP (original oil in place). Surfactant/polymer flooding targets these bypassed oil left after waterflood by reducing water mobility and oil/water interfacial tension. The complexity and uncertainty of reservoir characterization make the design and implementation of a robust and effective surfactant/polymer flooding to be quite challenging. Accurate numerical simulation prior to the field surfactant/polymer flooding is essential for a successful design and implementation of surfactant/polymer flooding. A recently developed unified polymer viscosity model was implemented into our existing polymer module within our in-house reservoir simulator, the Implicit Parallel Accurate Reservoir Simulator (IPARS). The new viscosity model is capable of simulating not only the Newtonian and shear-thinning rheology of polymer solution but also the shear-thickening behavior, which may occur near the wellbore with high injection rates when high molecular weight Partially Hydrolyzed Acrylamide (HPAM) polymers are injected. We have added a full capability of surfactant/polymer flooding to TRCHEM module of IPARS using a simplified but mechanistic and user-friendly approach for modeling surfactant/water/oil phase behavior. The features of surfactant module include: 1) surfactant component transport in porous media; 2) surfactant adsorption on the rock; 3) surfactant/oil/water phase behavior transitioned with salinity of Type II(-), Type III, and Type II(+) phase behaviors; 4) compositional microemulsion phase viscosity correlation and 5) relative permeabilities based on the trapping number. With the parallel capability of IPARS, commercial scale simulation of surfactant/polymer flooding becomes practical and affordable. Several numerical examples are presented in this dissertation. The results of surfactant/polymer flood are verified by comparing with the results obtained from UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability and scalability are also demonstrated. Advisors/Committee Members: Delshad, Mojdeh (advisor), Wheeler, Mary F. (Mary Fanett) (advisor), Balhoff, Matthew T. (committee member), Arbogast, Todd J. (committee member), Dean, Rick H. (committee member).

Subjects/Keywords: Surfactant/polymer flooding; Non-Newtonian fluid; Phase behavior; Parallel computation

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APA (6^th Edition):

Yuan, C. (2012). Commercial scale simulations of surfactant/polymer flooding. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-08-401

Chicago Manual of Style (16^th Edition):

Yuan, Changli. “Commercial scale simulations of surfactant/polymer flooding.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2012-08-401.

MLA Handbook (7^th Edition):

Yuan, Changli. “Commercial scale simulations of surfactant/polymer flooding.” 2012. Web. 18 Jan 2021.

Vancouver:

Yuan C. Commercial scale simulations of surfactant/polymer flooding. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-401.

Council of Science Editors:

Yuan C. Commercial scale simulations of surfactant/polymer flooding. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-08-401

27. Povich, Timothy James. Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport.

Degree: PhD, Computational and Applied Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-12-6504

► Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand… (more)

▼ Coastal regions are the most densely populated regions of the world. The populations of these regions continue to grow which has created a high demand for water that stresses existing water resources. Coastal aquifers provide a source of water for coastal populations and are generally part of a larger system where freshwater aquifers are hydraulically connected with a saline surface-water body. They are characterized by salinity variations in space and time, sharp freshwater/saltwater interfaces which can lead to dramatic density differences, and complex groundwater chemistry. Mismanagement of coastal aquifers can lead to saltwater intrusion, the displacement of fresh water by saline water in the freshwater regions of the aquifers, making them unusable as a freshwater source. Saltwater intrusion is of significant interest to water resource managers and efficient simulators are needed to assist them. Numerical simulation of saltwater intrusion requires solving a system of flow and transport equations coupled through a density equation of state. The scale of the problem domain, irregular geometry and heterogeneity can require significant computational resources. Also, modeling sharp transition zones and accurate flow velocities pose numerical challenges. Discontinuous Galerkin (DG) finite element methods (FEM) have been shown to be well suited for modeling flow and transport in porous media but a fully coupled DG formulation has not been applied to the variable density flow and transport model. DG methods have many desirable characteristics in the areas of numerical stability, mesh and polynomial approximation adaptivity and the use of non-conforming meshes. These properties are especially desirable when working with complex geometries over large scales and when coupling multi-physics models (e.g. surface water and groundwater flow models). In this dissertation, we investigate a new combined local discontinuous Galerkin (LDG) and non-symmetric, interior penalty Galerkin (NIPG) formulation for the non-linear coupled flow and solute transport equations that model saltwater intrusion. Our main goal is the formulation and numerical implementation of a robust, efficient, tightly-coupled combined LDG/NIPG formulation within the Department of Defense (DoD) Proteus Computational Mechanics Toolkit modeling framework. We conduct an extensive and systematic code and model verification (using established benchmark problems and proven convergence rates) and model validation (using experimental data) to verify accomplishment of this goal. Lastly, we analyze the accuracy and conservation properties of the numerical model. More specifically, we derive an a priori error estimate for the coupled system and conduct a flow/transport model compatibility analysis to prove conservation properties. Advisors/Committee Members: Dawson, Clinton N. (advisor), Gamba, Irene M. (committee member), Arbogast, Todd (committee member), Ghattas, Omar (committee member), Hesse, Marc (committee member).

Subjects/Keywords: Variable density flow; Discontinuous Galerkin finite elements methods; Saltwater intrusion

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APA (6^th Edition):

Povich, T. J. (2012). Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-12-6504

Chicago Manual of Style (16^th Edition):

Povich, Timothy James. “Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2012-12-6504.

MLA Handbook (7^th Edition):

Povich, Timothy James. “Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport.” 2012. Web. 18 Jan 2021.

Vancouver:

Povich TJ. Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-12-6504.

Council of Science Editors:

Povich TJ. Discontinuous Galerkin (DG) methods for variable density groundwater flow and solute transport. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-12-6504

28. Yu, Xiang, 1984-. Utility maximization with consumption habit formation in incomplete markets.

Degree: PhD, Mathematics, 2012, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2012-05-5590

► This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time… (more)

▼ This dissertation studies a class of path-dependent stochastic control problems with applications to Finance. In particular, we solve the open problem of the continuous time expected utility maximization with addictive consumption habit formation in incomplete markets under two independent scenarios. In the first project, we study the continuous time utility optimization problem with consumption habit formation in general incomplete semimartingale financial markets. Introducing the set of auxiliary state processes and the modified dual space, we embed our original problem into an abstract time-separable utility maximization problem with a shadow random endowment on the product space. We establish existence and uniqueness of the optimal solution using convex duality by defining the primal value function as depending on two variables, i.e., the initial wealth and the initial standard of living. We also provide market independent sufficient conditions both on the stochastic discounting processes of the habit formation process and on the utility function for the well-posedness of our original optimization problem. Under the same assumptions, we can carefully modify the classical proofs in the approach of convex duality analysis when the auxiliary dual process is not necessarily integrable. In the second project, we examine an example of the optimal investment and consumption problem with both habit-formation and partial observations in incomplete markets driven by It\^o processes. The individual investor develops addictive consumption habits gradually while only observing the market stock prices but not the instantaneous rates of return, which follow an Ornstein-Uhlenbeck process. Applying the Kalman-Bucy filtering theorem and Dynamic Programming arguments, we solve the associated Hamilton-Jacobi-Bellman(HJB) equation fully explicitly for this path dependent stochastic control problem in the case of power utility preferences. We provide the optimal investment and consumption policy in explicit feedback form using rigorous verification arguments. Advisors/Committee Members: Sîrbu, Mihai (advisor), Arbogast, Todd (committee member), Bayraktar, Erhan (committee member), Tompaidis, Stathis (committee member), Zariphopoulou, Thaleia (committee member), Zitkovic, Gordan (committee member).

Subjects/Keywords: Time non-separable utility maximization; Consumption habit formation; Convex duality; Auxiliary processes; Incomplete markets; Kalman-Bucy filtering; Verification lemma

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yu, Xiang, 1. (2012). Utility maximization with consumption habit formation in incomplete markets. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2012-05-5590

Chicago Manual of Style (16^th Edition):

Yu, Xiang, 1984-. “Utility maximization with consumption habit formation in incomplete markets.” 2012. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2012-05-5590.

MLA Handbook (7^th Edition):

Yu, Xiang, 1984-. “Utility maximization with consumption habit formation in incomplete markets.” 2012. Web. 18 Jan 2021.

Vancouver:

Yu, Xiang 1. Utility maximization with consumption habit formation in incomplete markets. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2012. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2012-05-5590.

Council of Science Editors:

Yu, Xiang 1. Utility maximization with consumption habit formation in incomplete markets. [Doctoral Dissertation]. University of Texas – Austin; 2012. Available from: http://hdl.handle.net/2152/ETD-UT-2012-05-5590

University of Texas – Austin

29. Leger, Nicholas Matthew. A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method.

Degree: PhD, Mathematics, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-05-1305

► We present a mathematical study of two conservative systems in fluid mechanics. First, we study a fragmentation model for sprays. The model takes into account… (more)

Subjects/Keywords: Shocks; Conservation laws; Relative entropy; Stability; Sprays; Fluid-particle model

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Leger, N. M. (2010). A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-05-1305

Chicago Manual of Style (16^th Edition):

Leger, Nicholas Matthew. “A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed January 18, 2021. http://hdl.handle.net/2152/ETD-UT-2010-05-1305.

MLA Handbook (7^th Edition):

Leger, Nicholas Matthew. “A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method.” 2010. Web. 18 Jan 2021.

Vancouver:

Leger NM. A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2021 Jan 18]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-1305.

Council of Science Editors:

Leger NM. A fragmentation model for sprays and L² stability estimates for shockes solutions of scalar conservation laws using the relative entropy method. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-1305

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