Finite volume schemes for a nonlinear hyperbolic conservation law with a flux function involving discontinuous coefficients - Archive ouverte HAL Access content directly
Journal Articles International Journal on Finite Volumes Year : 2006

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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Dates and versions

hal-01114200 , version 1 (08-02-2015)

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  • HAL Id : hal-01114200 , version 1

Cite

Florence Bachmann. Finite volume schemes for a nonlinear hyperbolic conservation law with a flux function involving discontinuous coefficients. International Journal on Finite Volumes, 2006, 3 (1), pp.1-38. ⟨hal-01114200⟩
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