Finite volume schemes for a nonlinear hyperbolic conservation law with a flux function involving discontinuous coefficients

Abstract : A model for two phase flow in porous media with distinct permeabilities leads to a nonlinear hyperbolic conservation law with a discontinuous flux function. In this paper, for such a problem, the notion of entropy solution is presented and existence and convergence of a finite volume scheme are proved. No hypothesis of convexity or genuine nonlinearity on the flux function is assumed, which is a new point in comparison with previous works. As the trace of the solution along the line of discontinuity of the flux function cannot be considered , this problem is more complex. To illustrate these results, some numerical tests are presented.
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International Journal on Finite Volumes, Institut de Mathématiques de Marseille, AMU, 2006, 3 (1), pp.1-38
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Florence Bachmann. Finite volume schemes for a nonlinear hyperbolic conservation law with a flux function involving discontinuous coefficients. International Journal on Finite Volumes, Institut de Mathématiques de Marseille, AMU, 2006, 3 (1), pp.1-38. 〈hal-01114200〉

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