Finite element solution strategies for large-scale flow simulations

Large-scale flow simulation strategies involving implicit finite element formulations are described in the context of incompressible flows. The stabilized space-time formulation for problems involving moving boundaries and interfaces is presented, followed by a discussion of mesh moving schemes. The methods of solution of large linear systems of equations are reviewed, and an implementation of the entire finite element code, permitting the use of totally unstructured meshes, on a massively parallel supercomputer is considered. As an example, this methodology is applied to a flow problem involving three-dimensional simulation of liquid sloshing in a tank subjected to vertical vibrations.