A CeVeFE DDFV scheme for discontinuous anisotropic permeability tensors

Yves Coudière (1) , Florence Hubert (2) , Gianmarco Manzini (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche

In this work we derive a formulation for discontinuous diffusion tensor for the Discrete Duality Finite Volume (DDFV) framework that is exact for affine solutions. In fact, DDFV methods can naturally handle anisotropic or non-linear problems on general distorded meshes. Nonetheless, a special treatment is required when the diffusion tensor is discontinuous across an internal interfaces shared by two control volumes of the mesh. In such a case, two different gradients are considered in the two subdiamonds centered at that interface and the flux conservation is imposed through an auxiliary variable at the interface.

Mots clés: DDFV Schemes; Anisotropic problems

Domaines: Analyse numérique [math.NA]

Yves Coudière, Florence Hubert, Gianmarco Manzini. A CeVeFE DDFV scheme for discontinuous anisotropic permeability tensors. Finite Volume for Complex Applications VI, Jun 2011, Praha, Czech Republic. pp.283--292. ⟨hal-00580540⟩