Abstract
We consider the solution of a two-phase miscible displacement problem on dynamic adaptive meshes using the mimetic finite difference method. The mimetic finite difference method is employed to discretize the Darcy law and the mass fraction advection-dispersion equation. We propose modifications to the mimetic finite difference method: to reproduce two-point flux approximation on -orthogonal grids and address degenerate advection-diffusion problems. We validate the method and demonstrate its applicability to the viscous fingering problem with adaptive mesh refinement.
| Original language | English |
|---|---|
| Pages (from-to) | 143-154 |
| Number of pages | 12 |
| Journal | Lobachevskii Journal of Mathematics |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2024 |
Keywords
- Adaptive mesh
- Advection-diffusion equation
- Mimetic finite difference
- Miscible displacement