An Adaptive Grid Method for a Non-Equilibrium PDE Model from Porous Media

Abstract

An adaptive grid method is applied to a PDE model from geo-hydrology. Due to the higher mixed-order derivative, non-monotone waves can appear which could represent similar structures as observed in laboratory experiments [5, 16, 18]. The effectiveness of the adaptive grid, which is based on a smoothed equidistribution principle, is shown compared to uniform grid simulations. On a uniform grid (numerical) oscillating non-monotone waves may appear which are not present in the adaptive grid.