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

2016/10/13 by Jessica Bosch, Bosch, Jessica, Christian Kahle +3
Engineering · Materials Science · #35K55 #35Q30 #65F08 #65F10 #65F50 #65N22 #74S05 #82C26 #93C20 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1610.03991

openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

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