An Adaptive Grid Method for a Non-Equilibrium PDE Model from Porous Media (Journal of Mathematical Study, 2015)
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 whichcould represent similar structures as observed in laboratory experiments [5, 16, 18].The effectiveness of the adaptive grid, which is based on a smoothed equidistributionprinciple, is shown compared to uniform grid simulations. On a uniform grid (numerical)oscillating non-monotone waves may appear which are not present in the adaptivegrid.
Keywords: Adaptive grids; Method of lines; Dynamical systems; Travelling waves; Monotonicity; Porous media; Water saturation.