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Joel Silas

Joel Silas (MS, Mathematical Sciences)

Monday, November 16, 2026
1 p.m.
Fisher
Advisor: Yang Yang
Title: Computational Study of Finite Difference and Second-Order Bound-Preserving Discontinuous Galerkin Methods for Reactive Transport and Wormhole Propagation in Porous Media
Abstract: This report compares two established discretizations for reactive transport and wormhole propagation in porous media: first-order upwind finite differences (FD) and second-order bound-preserving discontinuous Galerkin (DG) methods. The model couples Darcy flow, acid transport, reaction, porosity evolution, and porosity-dependent permeability. The DG method uses rectangular Q1 elements, numerical fluxes, strong-stability-preserving Runge–Kutta time stepping, and a cellwise scaling limiter. Separate refinement studies assess each method against its expected convergence order. Discontinuous-transport and wormhole simulations examine admissible concentration and porosity, oscillation control, front sharpness, and dissolution-channel localization. The upwind FD method provides a robust baseline but introduces numerical diffusion; the limited DG method controls nonphysical extrema at selected points while resolving localized structures. The study evaluates these established methods without claiming a new scheme or a universal accuracy ranking.

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