Two-point stress approximation: A simple and robust finite volume method for linearized (poro-)elasticity and Stokes flow

A new minimal, cell-centered finite volume discretization for isotropic linearized elasticity that remains stable in the incompressible limit. Its simplicity and robustness make it ideal for coupling with flow solvers in poroelastic simulations.

Published:

Meshes
illustrations of admissible meshes. We emphasize in particular A: Simplexes, B: Non-convex, C: Parallelogram, D: Local grid refinement, E: Rectangles, and F: An Archimedean tiling. Face orthogonality is indicated by the right-angle symbol. Figure from https://www.sciencedirect.com/science/article/pii/S0898122125003244 Photo: Jan Martin Nordbotten

In the context of finite volume methods for elastic materials, the Multi-Point Stress Approximation (MPSA) is a commonly used method. In the recent paper Two-point stress approximation: A simple and robust finite volume method for linearized (poro-)elasticity and Stokes flow (external link) by Jan Martin Nordbotten and Eirik Keilegavlen, an alternative method was introduced. The new method is a simple, robust two-point finite volume method.

  • It only uses cell-centered variables with a stencil that only uses the two neighboring cells.
  • The method is applicable in the incompressible Stokes' limit, meaning it can be used when coupling flow and poroelastic materials.
  • It is tested on numerical examples in 3D.

Publication details

Authors: Jan Martin Nordbotten and Eirik Keilegavlen.

Link to paper. (external link)