Date of Award

2026-05-01

Degree Name

Master of Science

Department

Computational Science

Advisor(s)

Son-Young Yi

Abstract

Classic approaches to modeling fluid flow in porous media rely on Darcy's Law, which assumes a linear relationship between volumetric flow rate and the pressure gradient. However, in recent years, applications such as enhanced geothermal systems have highlighted the need to model nonlinear flow behavior, since experimental and observational data show that, once flow velocity exceeds a certain threshold, the relationship between velocity and macroscopic pressure gradient becomes nonlinear. This requires alternative models that more accurately capture the physical behavior of these systems.The Darcy-Forchheimer model provides one such alternative by introducing a nonlinear velocity-pressure relationship. However, this nonlinearity creates additional mathematical and computational challenges, particularly in heterogeneous media and in regimes where nonlinear effects are strong.

In this thesis, we solve the Darcy-Forchheimer equation using a mixed finite element method, with the nonlinear system treated by Picard fixed-point iteration. Because the Picard method can require many iterations to converge under strong nonlinearities or in highly heterogeneous permeability structures, we apply Anderson Acceleration to improve computational efficiency. The accelerated method achieves substantially faster convergence while preserving the structure of the mixed finite element formulation. Finally, we compare this traditional numerical framework with neural-network-based approaches for modeling nonlinear flow in porous media.

Language

en

Provenance

Received from ProQuest

File Size

90 p.

File Format

application/pdf

Rights Holder

Nate McNair

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