Hybrid mimetic finite-difference and virtual element formulation for coupled poromechanics
arXiv:2010.15470 · doi:10.1016/j.cma.2021.113917
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.
arXiv comment25 pages, 17 figures
References in corpus (12)
- A Virtual Element Method for elastic and inelastic problems on polytope meshes
- A unified approach to Mimetic Finite Difference, Hybrid Finite Volume and Mixed Finite Volume methods
- Space-time finite element approximation of the Biot poroelasticity system with iterative coupling
- Parameter-robust stability of classical three-field formulation of Biot's consolidation model
- New stabilized discretizations for poroelasticity and the Stokes' equations
- Stable cell-centered finite volume discretization for Biot equations
- Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media
- A Scalable Multigrid Reduction Framework for Multiphase Poromechanics of Heterogeneous Media
- Efficient solvers for hybridized three-field mixed finite element coupled poromechanics
- Gradient discretization of two-phase flows coupled with mechanical deformation in fractured porous media
- Multigrid reduction preconditioning framework for coupled processes in porous and fractured media
- The mixed virtual element method for grids with curved interfaces
Cited by in corpus (4)
- A phase-field model for hydraulic fracture nucleation and propagation in porous media
- A bubble VEM-fully discrete polytopal scheme for mixed-dimensional poromechanics with frictional contact at matrix fracture interfaces
- A new family of semi-implicit Finite Volume / Virtual Element methods for incompressible flows on unstructured meshes
- Multigrid reduction preconditioning framework for coupled processes in porous and fractured media