Modeling Chemotactic Waves in Saturated Porous Media using Adaptive Mesh Refinement

Abstract

Bacterial transport is heavily influenced by chemical gradients and interfaces that exist in the subsurface. The main aim of this article is to describe a method of simulating the propagation of a traveling bacterial wave in a contaminated region and the resulting degradation of the contaminant. The presence of the chemotactic term and the relatively small bacterial diffusion means that the wave contains a very sharp wavefront. We, therefore, use an upwind conservative numerical scheme to obtain accurate and numerically stable solutions. The accuracy of the method is verified by comparisons with an exact one-dimensional solution of a simplified problem to give the same wavespeed. The method is then used to simulate the propagation of a realistic chemotactic wave in one dimension. We then use adaptive mesh refinement (AMR) to compute the propagation of chemotactic waves in two dimensions using the simplified model calibrated to give the same wavespeed as the full model.