A CeVeFE DDFV scheme for discontinuous anisotropic permeability tensors

Abstract : 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.
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Communication dans un congrès
J. Fort, J. Furst, J. Halama, R. Herbin, F. Hubert. Finite Volume for Complex Applications VI, Jun 2011, Praha, Czech Republic. Springer, pp.283--292, 2011
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Yves Coudière, Florence Hubert, Gianmarco Manzini. A CeVeFE DDFV scheme for discontinuous anisotropic permeability tensors. J. Fort, J. Furst, J. Halama, R. Herbin, F. Hubert. Finite Volume for Complex Applications VI, Jun 2011, Praha, Czech Republic. Springer, pp.283--292, 2011. 〈hal-00580540〉

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