Abstract
The present work is devoted to the numerical approximation of the solutions of the inviscid limit of multipressure Navier-Stokes equations in several space dimensions. The nonconservation form of the Euler-like limit model makes the shock solutions sensitive with respect to the underlying small scales and then challenges their numerical approximation. In particular, classical algorithms fail in producing good numerical results. Here we are mainly concerned with (large time stepping) implicit numerical strategies. We first exhibit a set of generalized jump conditions satisfied by the shock solutions and well-suited to derive a time-implicit scheme. We then devise a linearized time-implicit solver for the sake of efficiency. This solver is shown to preserve the positivity of each internal energy $\epsilon_i$ provided that the total internal energy stays positive.
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