A Structure-Preserving Numerical Method for Quasi-Incompressible Navier–Stokes–Maxwell–Stefan systems

A conforming finite element scheme with mixed explicit–implicit time discretization for quasi-incompressible Navier–Stokes–Maxwell–Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the Navier–Stokes equations, together with a quasi-incompressibility constraint, coupled with the cross-diffusion Maxwell–Stefan equations. The numerical scheme preserves the partial masses and the quasi-incompressibility constraint and dissipates the discrete energy. Numerical experiments in two space dimensions illustrate the convergence of the scheme and the structure-preserving properties.