Mathematikgebäude, Seminarraum E27

We present a phase-field model for multiphase flow of arbitrary number of immiscible incompressible fluids with variable densities and viscosities. The model consists of a system of variable density and viscosity Navier-Stokes equations coupled to multicomponent Cahn- Hilliard variational inequalities. The proposed formulation admits a natural energy law, exactly preserves physically meaningful constraints and allows for a straightforward modeling of surface tension effects. We propose a practical fully-discrete finite element approximation of the model which preserves the energy law and the associated physical constraints. In the case of matched densities we prove convergence of the numerical scheme towards a weak solution of the continuous model. As a by product of the convergence result we obtain existence of weak solutions. Furthermore, we propose a convergent iterative fixed-point algorithm for the solution of the discrete nonlinear system of equations and present various computational studies to demonstrate properties of the phase-field model.

Prof. Dr. Ľubomír Baňas

Universität Bielefeld