Scalar conservation laws with a flux function discontinuous in space are approximated using a Godunov-type method for which a convergence theorem is proved. The case where the flux functions at the interface intersect is emphasized. A very simple formula is given for the interface flux. A numerical comparison between the Godunov numerical flux and the upstream mobility flux is presented for two-phase flow in porous media. A consequence of the convergence theorem is an existence theorem for the solution of the scalar conservation laws under consideration.Furthermore, for regular solutions, uniqueness has been shown.
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Adimurthi et al. (2004) studied this question.
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