Parallel finite element computations in fluid mechanics

We provide an overview of the role of parallel finite element computations in fluid mechanics. We emphasize the class of flow problems involving moving boundaries and interfaces. Some of the computationally most challenging flow problems, such as fluid-object and fluid-structure interactions as well as free-surface and two-fluid flows, belong to this class. In the development of the methods targeting this class of problems, the computational challenges involved need to be addressed in such a way that 3D computation of complex applications can be carried out efficiently on parallel computers. This requirement has to be one of the key factors in designing various components of the overall solution approach, such as solution techniques for the discretized equations and mesh update methods for handling the changes in the spatial domain occupied by the fluid. This overview includes a description of how the computational challenges are addressed and how the computational schemes can be enhanced with special preconditioning techniques.