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

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

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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.

Author Details

Paul Andries Zegeling

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