A segregated algorithm for the solution of the Cahn-Hilliard equation in multiphase flows*

A segregated algorithm for the solution of the Cahn-Hilliard equation in multiphase flowsPhase field methods are gaining momentum in science and engineering to model multicomponent and multiphase systems thanks to their thermodynamically consistent formulation and the general smoothness of the fields. In fact, they provide a framework to include complex physical processes (such as phase-change) and result in less spurious oscillations when dealing with surface tension, compared to other methods like the volume of fluid. The Cahn-Hilliard equation is the principal governing equation in the phase field method as it results from a minimization of the free energy functional and thus includes all the relevant physical phenomena such as phase-change and surface tension forces. However, its solution is not straightforward as it is a fourth-order non linear partial differential equation. A number of explicit methods have been proposed in literature together with an implicit mixed formulation. Segregated implicit algorithms are seldom used due to stability issues.In this work, we present a novel segregated algorithm for the solution of the Cahn-Hilliard equation based on the incomplete block-Schur preconditioning technique. Performance and accuracy of the algorithm are compared against a block-coupled mixed formulation for a number of cases. We also illustrate several applications of the method to multiphase flows with phase change.