Mesh generation and update strategies for parallel computation of flow problems with moving boundaries and interfaces

We present strategies to update the mesh as the spatial domain changes its shape in computations of flow problems with moving boundaries and interfaces. These strategies are used in conjunction with the stabilized space-time finite element formulation introduced earlier for computation of flow problems with free surfaces, two-liquid interfaces, moving mechanical components, and fluid-structure and fluid-particle interactions. The implementation of this space-time method on parallel architectures, namely the CM-5, will also be presented in some detail, and relevant issues that arise from parallel computing will be discussed. In these mesh update strategies, based on the special and automatic mesh moving schemes, the frequency of remeshing is minimized to reduce the projection errors and to minimize the cost associated with mesh generation and parallelization set up. These costs could otherwise become overwhelming in 3D problems. A closely related topic to mesh update strategies is mesh generation, and methods for generating meshes on arbitrary geometries, in both 2D and 3D, will also be presented. We present several examples of these mesh update and mesh generation strategies being used in computation of incompressible flow problems.