Hybrid finite volume discretization of linear elasticity models on general meshes
Résumé
This paper presents a new discretization scheme for linear elasticity models using only one degree of freedom per face corresponding to the normal component of the displacement. The scheme is based on a piecewise constant gradient construction and a discrete variational formulation for the displacement field. The tangential components of the displacement field are eliminated using a second order linear interpolation. Our main motivation is the coupling of geomechanical models and porous media flows arising in reservoir or CO$_2$ storage simulations. Our scheme guarantees by construction the compatibility condition between the displacement discretization and the usual cell-centered finite volume discretization of the Darcy flow model. In addition it applies on general meshes, possibly non conforming such as Corner Point Geometries commonly used in reservoir and CO$_2$ storage simulations.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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