Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system
For researchers solving two-phase flow problems, this provides an efficient linear solver, but the method is incremental (preconditioning for an existing discretization).
The authors propose preconditioned Krylov subspace solvers for large sparse linear systems arising in a diffuse interface model for two-phase flows, demonstrating robustness to parameter changes.
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.