An explicit finite element scheme based on a two step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes Equations for a wide variety of flow problems. To obtain useful results for realistic problems one has to use grids with an extremely high density to get a good resolution of the interesting parts of a given flow. Since these details are often limited to small regions of the calculation domain, it is efficient to use unstructured grids to reduce the number of elements and grid points. As such calculations are very time consuming and inherently parallel the use of multiprocessor systems for this task seems to be a very natural idea. A common approach for parallelization is the division of a given grid, where the problem is the increasing complexity of this task for growing processor numbers. Here we present some general ideas for this kind of parallelization and details of a Parix implementation for Transputer networks. To improve the quality of the calculated solutions an adaptive grid refinement procedure was included. This extension leads to the necessity of a dynamic load balancing for the parallel version. An effective strategy for this task is presented and results for up to 1024~processors show the general suitability of our approach for massively parallel systems.
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