Abstract
We consider weak solutions of hyperbolic conservation laws assingular limits of solutions for associated complex regularizedproblems. We are interested in situations such thatundercompressive (Non-Laxian) shock waves occur in the limit. Inthis setting one can view the conservation law as a macroscaleformulation while the regularization can be understood as themicroscale model. With this point of view it appears naturalto solve the macroscale model by a heterogeneous multiscaleapproach in the sense of E&Engquist[7].We introduce a new mass-conserving numerical method based on thisconceptand test it on scalar model problems.This includes applications from phase transitiontheory as well as from two-phase flow in porous media.
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