Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics

TL;DR

This paper introduces a hybrid mimetic finite-difference and virtual element method for coupled poromechanics that is convergent on complex, distorted meshes, with stabilization and scalable solution strategies demonstrated on benchmarks.

Contribution

It develops a novel hybrid discretization scheme for coupled poromechanics that handles complex meshes and prevents spurious pressure modes, with an efficient solver.

Findings

Convergent on highly distorted meshes

Prevents spurious pressure modes in incompressible problems

Demonstrated accuracy and efficiency on benchmark problems

Abstract

We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly distorted cells with arbitrary shapes. We use a local pressure-jump stabilization method based on unstructured macro-elements to prevent the development of spurious pressure modes in incompressible problems approaching undrained conditions. A scalable linear solution strategy is obtained using a block-triangular preconditioner designed specifically for the saddle-point systems arising from the proposed discretization. The accuracy and efficiency of our approach are demonstrated numerically on two-dimensional benchmark problems.