Degree

Doctor of Philosophy (PhD)

Department

Department of Civil and Environmental Engineering

Document Type

Dissertation

Abstract

Accurate prediction of subsurface flow and transport is crucial for stormwater management, groundwater contamination assessment, and geologic carbon storage. Standard Galerkin finite element methods (FEM) may violate the discrete maximum principle and produce non-physical oscillations near fronts, whereas commonly used stabilization approaches, such as mass lumping and upwinding, improve robustness at the cost of excessive numerical diffusion and reduced accuracy. This work develops high-resolution, higher-order FEM methodologies that preserve physical bounds while retaining accuracy, and demonstrates their applicability to variably saturated flow, contaminant transport, and multiphysics carbon capture and storage (CCS) modeling within the Proteus framework.

First, a bound-preserving Flux-Corrected Transport (FCT) formulation is developed to solve Richards' equation (RE) and simulate infiltration in variably saturated media on unstructured meshes. The method combines a monotone low-order scheme with a higher-order scheme through limited anti-diffusive fluxes that suppress spurious oscillations and enforce a discrete maximum principle across coarse grid resolutions. The approach is verified through convergence studies against available analytical solutions and is applied to infiltration scenarios relevant to stormwater control measures such as raingardens and bioswales.

Second, a coupled flow-and-transport modeling capability is developed for transient flow and solute transport in variably saturated porous media. The flow field is computed using the mixed form of RE to ensure mass conservation, and solute transport is modeled by a variable-density advection--diffusion equation (ADE). A split-operator, one-way coupling strategy is implemented in which the seepage velocity from the RE solution drives advective transport. To address oscillations arising in both flow and transport near sharp fronts, the framework combines stabilizations with FCT corrections to recover high accuracy without oscillations. Validation is performed on benchmark problems such as the Henry and Elder problems.

Finally, a multicomponent flow-and-transport model in porous media is developed to simulate CO2 injection. The formulation enforces mass conservation for a multiphase problem that incorporates Darcy flow with advective and dispersive transport processes needed to represent CO2 injection, migration, trapping, and long-term containment. The coupled system is simulated against the FluidFlower benchmark. The resulting framework is then applied toward simulating CO2 transport in Lake Maurepas.

Date

7-26-2026

Committee Chair

Kees, Christopher E.

LSU Acknowledgement

1

LSU Accessibility Acknowledgment

1

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