Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics. (English) Zbl 1506.74390
Summary: 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.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
Keywords:
poroelasticity; mimetic finite-difference; virtual element method; arbitrary polygonal meshesReferences:
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