An explicit finite element scheme based on a two step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes Equations on unstructured grids. Calculations on unstructured grids are inherently parallel and very time consuming so that speeding up the runtime is the main problem which had to be solved. We have implemented a parallel algorithm running under Helios for different array topologies based on an algorithm devoloped by experienced engineers for sequential computers. To get the desired linear speedup for many processors we had to implement an efficient load balancing strategy for the network that keeps all processors working at disjoint tasks. A first approach was an even distribution of the grid elements, with interprocessor communication to a limited number of neighbor processors. The resulting speedups for runs with up to 256 processors have shown on the one hand the general suitability of this approach and on the other hand the difficulties of dividing an unstructured grid for more than two or three dozens of processors. The resulting decrease of calculation times have made it possible to add an on-line visualization of the computational results on a graphic screen. So in contrast to a picture drawn by a plotter after the whole computation we get a graphical image of the evolving flow during the runtime of the algorithm.