TY - JOUR
T1 - An Adaptive Grid Method for a Non-Equilibrium PDE Model from Porous Media
AU - Zegeling , Paul Andries
JO - Journal of Mathematical Study
VL - 2
SP - 187
EP - 198
PY - 2015
DA - 2015/06
SN - 48
DO - http://doi.org/10.4208/jms.v48n2.15.05
UR - https://global-sci.org/intro/article_detail/jms/9919.html
KW - Adaptive grids, Method of lines, Dynamical systems, Travelling waves, Monotonicity, Porous media, Water saturation.
AB - <p style="text-align: justify;">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.</p>