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We approximate a two--phase model by the compressible Navier-Stokes equationswith a singular pressure term. Up to a subsequence, these solutions are shownto converge to a global weak solution of the compressible system with thecongestion constraint studied for instance by P.L. Lions and N. Masmoudi [Annales I.H.P., 1999]. The paper is an extension of the previous resultobtained in one-dimensional setting by D. Bresch et al. [ C. R. Acad. SciencesParis, 2014] to the multi-dimensional case with heterogeneous barrier for thedensity.

Free/Congested Two-Phase Model from Weak Solutions to Multi-Dimensional Compressible Navier-Stokes Equations