High Performance Computing in Free Surface Fluid Flows

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The proposed research includes several interconnected areas of activity. First among them is the continuing developments of a general stabilized finite element method for incompressible fluid flows in the presence of moving boundaries, with particular emphasis on free surface and two-phase flows. The method is based on a stabilized space-time formulation, and is capable of handling large deformations of the domain. The velocity- pressure-stress formulation will be developed in parallel. It is a novel stabilized formulation for incompressible flows which is applicable to viscoelastic fluids. This research area will be merged into the space-time method development, to allow for numerical treatment of viscoelastic fluids in the presence of moving boundaries. Proposed finite element formulations result in large linear systems of equations. These systems will be solved implicitly using a GMRES iterative method. To improve the rate of convergence, efficient preconditioning techniques will be designed and test. Among others, techniques combining the Clustered Element-By-Element and Multigrid approaches will be examined. All implementation work will concentrate on massively parallel architectures.