Preconditioning for incompressible flows with freesurfaces and twofluid interfaces
Abstract
We investigate preconditioners for solving steady or implicitunsteady arbitraryLagrangianEulerian movingmesh formulations of incompressible freesurface and interfacial flow problems. The solution for the flow is obtained using the artificial compressibility method combined with a multigrid cycle. To find the surface positions in a freesurface problem, we use an iteration that is quasiphysical with the position of the freesurface driven by the kinematic condition. By modifying the fluxes through the freesurface and also using an iterative freesurface time step that is different from the flow timestep, we are able to obtain convergence rates that are almost indistinguishable from those of a flow without a freesurface. This is true in the limits of both large and small surface stresses such as gravity or surface tension and also for all flow conditions (high or low Reynolds number or small implicit CourantFriedrichsLewy number). For interfacial flows, the freesurface preconditioner is extended by using a mass averaging technique. The iterative flow timestep at the interface is a mass average of the time step for the flow conditions on either side of the interface and the iterative time step for the kinematic condition is also based on massaverage quantities. We verify that this technique produces the correct results in the limits of identical fluids or a freesurface flow. We also verify that it produces wellconditioned results when the characteristic time scales of the two fluids are very different.
 Publication:

Journal of Computational Physics
 Pub Date:
 July 2005
 DOI:
 10.1016/j.jcp.2005.01.012
 Bibcode:
 2005JCoPh.207..282H