Parallel computing of high-speed compressible flows using a node-based finite-element method

An e cient parallel computing method for high-speed compressible ows is presented. The numerical analysis of ows with shocks requires very ne computational grids and grid generation requires a great deal of time. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed seamlessly in parallel in terms of nodes. Local nite-element mesh is generated robustly around each node, even for severe boundary shapes such as cracks. The algorithm and the data structure of nite-element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coe cient matrix. The inter-processor communication is minimized by renumbering the nodal identi cation number using ParMETIS. The numerical scheme for high-speed compressible ows is based on the two-step Taylor–Galerkin method. The proposed method is implemented on distributed memory systems, such as an Alpha PC cluster, and a parallel supercomputer, Hitachi SR8000. The performance of the method is illustrated by the computation of supersonic ows over a forward facing step. The numerical examples show that crisp shocks are e ectively computed on multiprocessors at high e ciency