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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 187-198 |
| Number of pages | 12 |
| Journal | Journal of Mathematical Study |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2015 |
Keywords
- Adaptive grids
- Method of lines
- Dynamical systems
- Travelling waves
- Monotonicityx
- Porous media
- Water saturation