J. Math. Study, 48 (2015), pp. 187-198.
Published online: 2015-06
[An open-access article; the PDF is free to any online user.]
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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.
}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v48n2.15.05}, url = {http://global-sci.org/intro/article_detail/jms/9919.html} }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.