Semi-Godunov schemes for multiphase flows in porous media

Authors:
K. H. Karlsen;S. Mishra;N. H. Risebro
Affiliations:
Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;Centre of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway
Venue:
Applied Numerical Mathematics
Year:
2009

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Abstract

We describe a class of finite volume schemes for 2x2 systems of conservations laws based on a ''local'' decomposition of the system into a series of single conservation laws but with discontinuous coefficients. The resulting schemes are based on Godunov type solvers of the reduced equations. These schemes are very easy to implement since they do not use detailed information about the eigenstructure of the full system. We illustrate the efficiency of the schemes on a variety of numerical experiments focusing on three-phase flows in porous media and show that they are robust and approximate the flow very well, even in the presence of gravity.