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arXiv · 2010.15470

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

Andrea Borio·François Hamon·Nicola Castelletto·Joshua A. White·Randolph R. Settgast
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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.

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Andrea Borio, François Hamon, Nicola Castelletto, Joshua A. White, Randolph R. Settgast. 2020-10-29. Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics. https://doi.org/10.1016/j.cma.2021.113917

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