Incompressible two-phase flow: Diffuse interface approach for large density ratios, grid resolution study, and 3D patterned substrate wetting problem

摘要

We explore numerical simulations of incompressible and immiscible two-phase flows. The description of the fluid-fluid interface is captured via a diffuse interface approach. The two phase fluid system is represented by a coupled Cahn-Hilliard Navier-Stokes set of equations. We discuss challenges and solution approaches to solving this coupled set of equations using a SUPG stabilized finite element formulation, especially in the case of a large density ratio between the two fluids. Specific features that enabled efficient solution of the equations include: (i) a conservative form of the convective term in the Cahn-Hilliard equation which ensures conservation of mass of both fluid components; (ii) a continuous formula to compute the interfacial surface tension which results in lower requirement on the spatial resolution of the interface; and (iii) a four-step fractional scheme to decouple pressure from velocity in the Navier-Stokes equation, which provides an efficient time discretization. These are integrated with standard streamline upwind Petrov-Galerkin (SUPG) stabilization to avoid spurious oscillations.