The finite element method for Cahn-Hilliard-Navier-Stokes equations

The Cahn-Hilliard equations provides a model of phase transitions when two or more immiscible fluids interact. When coupled with the Navier-Stokes equations we obtain a model fro the dynamics of multiphase flow. This model takes into account the viscosity and densities of the various fluids present.

A finite element discretisation of the variable density Cahn-Hilliard-Navier-Stokes equations is presented. An analysis of the discretisation and a reliable efficient numerical solution method are presented.