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Symmetry and M-matrix issues for the O-method on an unstructured grid. (English) Zbl 1094.76551

Summary: More sophisticated discretization methods than the traditional control-volume finite-difference methods, have been proposed by Aavatsmark et al. in recent papers for solving the mass balance equations for porous media flow. These methods are based on a local representation of fluxes across cell-edges of control volumes (CVs). This paper will focus on mathematical properties of the discrete operator that arises when an elliptic term of the form \(-\nabla \cdot ({\mathbf K}\nabla p)\) is discretized based on these discretization principles.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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