Massively parallel finite element computation of 3d flows - mesh update strategies in computation of moving boundaries and interfaces°

Abstract

This chapter describes the parallel implicit finite element computations of compressible and incompressible flows with the Connection Machine (CM)—CM-200 and CM-5. The parallel implementations are based on the assumption that the mesh is unstructured. The computations of flow problems involving moving boundaries and interfaces are achieved by using the deformable-spatial-domain or stabilized space-time method. In this method, with special mesh update strategies, the frequency of remeshing is minimized. This avoids the projection errors generated by remeshing and also avoids the cost associated with repeated mesh generation and parallelization setup. This method and its implementation on the massively parallel supercomputers provide a new capability to solve a large class of practical problems involving free surfaces, two-liquid interfaces, and fluid-structure interactions. Now 3D incompressible flow computations can be carried out at sustained speeds of up to 7.0 GigaFLOPS on the CM-5. The 3D compressible flow computations are carried out at sustained speeds of up to 12.2 GigaFLOPS on the CM-5. This parallel performance is significant in the sense that now there is a new level of computational capability in finite element solution of 3D flow problems. Several 3D flow problems are solved using these parallel and update mesh strategies. The chapter discusses the computation of incompressible flow occurring between two concentric cylinders, sloshing in a liquid-filled container subjected to vertical vibrations, and supersonic flow past a delta-wing.