Semester of Graduation

Summer 2023

Degree

Master of Civil Engineering (MCE)

Department

Department of Civil & Environmental Engineering

Document Type

Thesis

Abstract

Simulating the infiltration process in variably saturated media by solving Richards' Equation (RE) remains a computationally challenging task. The degenerate parabolic nature of RE, along with the strongly nonlinear coefficients, makes it very difficult to obtain accurate solutions with conventional numerical methods unless highly refined meshes are used. That is, in the conventional Finite Element Method (FEM), the grid size has to be fine enough to ensure convergence and limit non-physical oscillations, which is computationally expensive. This research aims to develop a second-order accurate FEM discretization with no non-physical oscillations for RE on unstructured meshes which will converge faster than existing non-oscillatory first-order schemes and maintain these features independently of mesh quality and/or material anisotropy.

In this work, the mixed form of the RE is discretized using standard and recently developed Finite Element Methods. Modified Picard and Newton iterations are used to solve the nonlinear algebraic systems, as they are known to converge faster than the conventional Picard iteration. Mass lumping and upwinding of relative permeability are employed to construct a method with a local discrete maximum principle and hence global bound preservation. However, the accuracy is compromised with this stabilizing technique due to the extra numerical diffusion introduced in the lower-order scheme. Therefore, an anti-diffusive term is added to the lower-order solution using the Flux Corrected Transport (FCT) method. This higher-order scheme then enforces the discrete maximum principle like the low-order scheme while converging at the same rate as the Standard Galerkin method but with much lower error on coarse grids.

Date

7-19-2023

Committee Chair

Kees, Christopher E

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