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

Verdière, S.; Vignal, M. H.

Numer. Math. 80, No. 4, 601-639 (1998).

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

Keywords:

elliptic-hyperbolic system; heterogeneous cases with non-constant total mobility; convergence; error estimates