A fully coupled finite volume – virtual element scheme for poroelasticity problems in variably saturated porous media

A fully coupled finite volume – virtual element discretization scheme for the three-dimensional unsaturated poroelasticity equations is presented. The scheme is applicable to unstructured grids with polyhedral cells. Compared to previous work, the scheme overcomes 𝕂-orthogonality restriction by employing multipoint flux approximation, and is expanded to more complex partially saturated case adopting the Richards approach. Convergence properties and robustness with the respect to mesh types are examined.