Is this project an undergraduate, graduate, or faculty project?
Undergraduate
Project Type
individual
Campus
Daytona Beach
Authors' Class Standing
Maya McKean, Senior
Lead Presenter's Name
Maya McKean
Lead Presenter's College
DB College of Arts and Sciences
Faculty Mentor Name
Hemanta Kunwar
Abstract
We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was done to test the accuracy of our methods and models by comparing our numerical results with the exact solution for a selected manufactured solution, and by studying the reduction of numerical error under successive mesh refinements through FreeFEM. This framework for the dynamics of thermo-poroelastic systems provides a foundation to simulate complex processes that could occur in real world scenarios such as geothermal energy systems and sub-surface fluid transport applications.
Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?
No
Included in
Dynamic Systems Commons, Fluid Dynamics Commons, Numerical Analysis and Computation Commons
Numerical Modeling of Thermo-poroelasticity Using Finite Element Method
We propose a numerical method for solving and modeling thermo-poroelasticity problems using a finite element formulation. Thermo-poroelasticity models describe the coupled interaction between mechanical deformation, fluid flow, and heat transfer in specific materials or environments over time. These models demonstrate the evolution of displacement, pressure, and temperature; we compute these fields in this work using backward Euler time discretization and Enriched Galerkin finite element spatial discretization. For these computations we used FreeFEM, a partial differential equation solver that uses the finite element method, which produced our numerical results. We then compared these values with the expected analytical solution. This was done to test the accuracy of our methods and models by comparing our numerical results with the exact solution for a selected manufactured solution, and by studying the reduction of numerical error under successive mesh refinements through FreeFEM. This framework for the dynamics of thermo-poroelastic systems provides a foundation to simulate complex processes that could occur in real world scenarios such as geothermal energy systems and sub-surface fluid transport applications.