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Nonconforming finite volume methods. (English) Zbl 1036.76038

Summary: We extend and generalize recently proposed by many authors finite volume methods using the framework of mixed finite element methods. Proposed discretizations are defined for tensor permeabilities, they naturally produce a generalization of harmonic averaging, and are therefore well suited for heterogeneous and anisotropic media. They are locally mass conservative, and work on extremely flexible distorted meshes. Flux variables can be excluded locally, and the resulting discretizations for the pressures has the same stencils for Voronoi/PEBI grids as 2-point finite volume discretizations currently used in many simulators.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
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