Hybrid finite volume discretization of linear elasticity models on general meshes

Daniele Antonio Di Pietro (1) , Robert Eymard (2) , Simon Lemaire (1) , Roland Masson (3, 4)

1 IFPEN - IFP Energies nouvelles
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 COFFEE - COmplex Flows For Energy and Environment
4 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Mots clés: General meshes; Linear elasticity; Hybrid finite volumes

Domaines: Analyse numérique [math.NA]

Daniele Antonio Di Pietro, Robert Eymard, Simon Lemaire, Roland Masson. Hybrid finite volume discretization of linear elasticity models on general meshes. FVCA 6, Jun 2011, Prague, Czech Republic. pp.331-339, ⟨10.1007/978-3-642-20671-9_35⟩. ⟨hal-00795201⟩