Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system

TL;DR

This paper introduces a preconditioning strategy for large linear systems from a coupled Cahn--Hilliard Navier--Stokes model, enhancing solver efficiency and robustness in simulating two-phase flows.

Contribution

It proposes an effective preconditioner using Schur complement approximations for Krylov solvers applied to coupled Cahn--Hilliard Navier--Stokes systems, improving computational performance.

Findings

Preconditioner significantly reduces iteration counts.

Method demonstrates robustness across parameter variations.

Numerical experiments confirm efficiency gains.

Abstract

Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical Mathematics 99, pp. 151-171, 2016] developed a consistent discretization scheme for a thermodynamically consistent diffuse interface model for incompressible two-phase flows with different densities. At the heart of this method lies the solution of large and sparse linear systems that arise in a semismooth Newton method. We propose the use of preconditioned Krylov subspace solvers using effective Schur complement approximations. Numerical results illustrate the efficiency of our approach. In particular, our preconditioner is shown to be robust with respect to parameter changes.