An open area of research in computational fluid dynamics is the study of multi-fluid flows, phenomena which arise in many real-world fluid mechanics applications. In this talk, a phase field method for implicitly capturing the location of the interfaces in binarfluids will be discussed. This approach avoids the computational geometry complexities associated with fully Lagrangian or front-tracking Eulerian methods. These complexities are particularly pronounced on parallel computers.
Additionally, for flows with elastic membranes separating the fluids, a phase field formulation for the membrane stresses will be presented. The coupled membrane-fluid flow formulation is discretized by a combined continuous/discontinuous Galerkin method, which lends itself to an inherently parallel implementation. A block Schur complement preconditioner neutralizes the ill-conditioning of the coupled system due to disparate material properties. Parallel performance results demonstrate the efficacy of this preconditioner.