Preconditioning of a Coupled Cahn-Hilliard Navier-Stokes System (Communications in Computational Physics, 2018)
Recently, Garcke et al. [H. Garcke, M. Hinze, C. Kahle, Appl. Numer.Math. 99 (2016), 151–171)] developed a consistent discretization scheme for a thermodynamicallyconsistent diffuse interface model for incompressible two-phase flowswith different densities [H. Abels, H. Garcke, G. Grün, Math. Models Methods Appl.Sci. 22(3) (2012)]. At the heart of this method lies the solution of large and sparse linearsystems that arise in a semismooth Newton method. In this work we propose the use of preconditioned Krylov subspace solvers usingeffective Schur complement approximations. Numerical results illustrate the efficiencyof our approach. In particular, our preconditioner is shown to be robust with respectto parameter changes.