A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics*, **, ***

In this contribution, we investigate a diffuse interface model for quasi–incompressible flows. We determine corresponding sharp interface limits of two different scalings. The sharp interface limit is deduced by matched asymptotic expansions of the fields in powers of the interface. In particular, we study solutions of the derived system of inner equations and discuss the results within the general setting of jump conditions for sharp interface models. Furthermore, we treat, as a subproblem, the convective Cahn–Hilliard equation numerically by a Local Discontinuous Galerkin scheme.