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Numerical and theoretical study of a dual mesh method using finite volume schemes for two-phase flow problems in porous media. (English) Zbl 0912.76063
Summary: We examine two-phase flow problems in porous media. We use a dual mesh method to discretize this problem with finite volume schemes, and in a simplified case (elliptic-hyperbolic system) we prove the convergence of approximate solutions to the exact solutions. We study physically complex problems (heterogeneous cases with non-constant total mobility) and validate the method numerically on practical examples by computing error estimates for different test cases.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76T99 Multiphase and multicomponent flows
76S05 Flows in porous media; filtration; seepage
76M12 Finite volume methods applied to problems in fluid mechanics
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