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

Authors

  • Paul Andries Zegeling Department of Mathematics, Faculty of Science, Utrecht University, the Netherlands

DOI:

https://doi.org/10.4208/jms.v48n2.15.05

Keywords:

Adaptive grids, Method of lines, Dynamical systems, Travelling waves, Monotonicity, Porous media, Water saturation.

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.

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Published

2015-06-02

Issue

Vol. 48 No. 2 (2015)

Section

Articles