Coupling linear virtual element and non-linear finite volume methods for poroelasticity - Enchéry, Guillaume; Agélas, Léo (Comptes Rendus. Mécanique)
Solving poroelastic problems on a single grid is of paramount importance in the applications, especially in geosciences. However, these applications sometimes require to work with meshes made of distorted cells. With such grids, dedicated numerical schemes should be chosen to obtain consistent approximations for the stresses and for the fluxes. In J. Coulet et al. (2020), a coupled scheme based on the joint use of linear virtual elements and a two-point finite volume approximation on the same grid was proposed for Biot’s poroelastic problem. This work has also provided an analytic and numerical convergence study of the discrete coupled system. As a continuation, we here propose an extension of this study to more general polyhedral meshes and to heterogeneous anisotropic mobility tensors for the flow equations. At this occasion, a general finite-volume framework, which includes non-linear or sushi finite volume methods for instance, is introduced to extend this analysis.