Date of Award
2026-08-01
Degree Name
Master of Science
Department
Mathematical Sciences
Advisor(s)
Son-Young Yi
Abstract
This thesis focuses on the numerical approximation of a coupled Thermo-Hydro-Mechanical (THM) model with advective heat transport in heterogeneous media. The governing equations consist of three coupled equations: the momentum balance, the fluid mass balance, and the energy balance. The primary unknowns are displacement, pressure, and temperature. In this system, the fluid pressure determines the Darcy flux, and this flux transports heat through the advective term in the energy equation. Since the Darcy flux is computed numerically from the flow equation, the conservation properties of the flow approximation can affect the temperature solution. This effect is especially important when thermal diffusion is small relative to advective transport.
The main objective of this thesis is to investigate stabilization techniques for the continuous Galerkin (CG) method for temperature when heat transport is dominated by advection in a fully coupled nonlinear THM system. This thesis considers CG approximations for displacement and temperature, compares both CG and mixed finite element approximations for the flow variables, and examines two different stabilization methods: Streamline Upwind Petrov--Galerkin (SUPG) and combined mass lumping and algebraic upwinding for the temperature equation. Numerical experiments are conducted in both homogeneous and heterogeneous porous media to examine the effects of temperature stabilization and the Darcy flux approximation on the coupled THM systems.
Language
en
Provenance
Received from ProQuest
Copyright Date
2026-08
File Size
82 p.
File Format
application/pdf
Rights Holder
Payel Dey
Recommended Citation
Dey, Payel, "Stabilized Continuous Galerkin Methods For Heat Transport In Fully Coupled Nonlinear Thermo-Poroelasticity In Heterogeneous Porous Media" (2026). Open Access Theses & Dissertations. 4661.
https://scholarworks.utep.edu/open_etd/4661