Year: 2015
Author: Paul Andries Zegeling
Journal of Mathematical Study, Vol. 48 (2015), Iss. 2 : pp. 187–198
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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v48n2.15.05
Journal of Mathematical Study, Vol. 48 (2015), Iss. 2 : pp. 187–198
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Adaptive grids Method of lines Dynamical systems Travelling waves Monotonicity Porous media Water saturation.