Penalty-Projection Schemes for the Cahn-Hilliard Navier-Stokes Diffuse Interface Model of Two Phase Flow, and Their Connection to Divergence-Free Coupled Schemes

Abstract

We study and compare fully discrete numerical approximations for the Cahn-Hilliard-Navier-Stokes (CHNS) system of equations that enforce the divergence constraint in different ways, one method via penalization in a projection-type splitting scheme, and the other via strongly divergence-free elements in a fully coupled scheme. We prove a connection between these two approaches, and test the methods against standard ones with several numerical experiments. The tests reveal that CHNS system solutions can be efficiently and accurately computed with penalty-projection methods.