Volume 48, Issue 2
An Adaptive Grid Method for a Non-equilibrium PDE Model from Porous Media

Paul Andries Zegeling

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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  • 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 uniformgrid simulations. On a uniformgrid (numerical) oscillating non-monotone wavesmay appearwhich are not present in the adaptive grid.

  • Keywords

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

  • AMS Subject Headings

35Mxx, 35M11, 65Mxx, 65M20, 65M50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

P.A.Zegeling@uu.nl (Paul Andries Zegeling)

  • BibTex
  • RIS
  • TXT
@Article{JMS-48-187, author = {Zegeling , Paul Andries }, title = {An Adaptive Grid Method for a Non-equilibrium PDE Model from Porous Media}, journal = {Journal of Mathematical Study}, year = {2015}, volume = {48}, number = {2}, pages = {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 uniformgrid simulations. On a uniformgrid (numerical) oscillating non-monotone wavesmay appearwhich 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} }
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 KW - Method of lines KW - Dynamical systems KW - Travelling waves KW - Monotonicity KW - Porous media KW - Water saturation AB - 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 uniformgrid simulations. On a uniformgrid (numerical) oscillating non-monotone wavesmay appearwhich are not present in the adaptive grid.
Paul Andries Zegeling. (2019). An Adaptive Grid Method for a Non-equilibrium PDE Model from Porous Media. Journal of Mathematical Study. 48 (2). 187-198. doi:10.4208/jms.v48n2.15.05
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