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