Parallel finite element simulation of 3D incompressible flows: Fluid‐structure interactions

Massively parallel finite element computations of 3D, unsteady incompressible flows, including those involving fluid‐structure interactions, are presented. The computation with time‐varying spatial domains are based on the deforming spatial domain/stabilized space‐time (DSD/SST) finite element formulation. The capability to solve 3D problems involving fluid‐structure interactions is demonstrated by investigating the dynamics of a flexible cantilevered pipe conveying fluid. Computations of flow past a stationary rectangular wing at Reynolds number 1000, 2500 and 10⁷ reveal interesting flow patterns. In these computations, at each time step approximately 3 × 10⁶ non‐linear equations are solved to update the flow field. Also, preliminary results are presented for flow past a wing in flapping motion. In this case a specially designed mesh moving scheme is employed to eliminate the need for remeshing. All these computations are carried out on the Army High Performance Computing Research Center supercomputers CM‐200 and CM‐5, with major speed‐ups compared with traditional supercomputers. The coupled equation systems arising from the finite element discretizations of these large‐scale problems are solved iteratively with diagonal preconditioners. In some cases, to reduce the memory requirements even further, these iterations are carried out with a matrix‐free strategy. The finite element formulations and their parallel implementations assume unstructured meshes.