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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.

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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 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.

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