Flow Simulation With an Adaptive Finite Element Method on Massively Parallel Systems

. 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 calcul..

CFD with adaptive FEM on massively parallel systems

this paper we have introduced a parallelization for the calculation of fluid flow problems on unstructured grids. An existing sequential algorithm has been adjusted for Transputer systems under Parix and investigations on the parallelization of this problem have been made. For two logical processor topologies we have developed different grid division algorithms and compared them for some benchmark problems. The grid topology has shown its superiority over the pipe topology. This was expected since a two-dimensional topology must be better suited for two-dimensional grids than a one-dimensional topology which is not scalable for large processor numbers. The speed-up measurements on a 1024 Transputer cluster showed the general usefulness of the choosen approach for massively parallel systems. Further, we presented an adaptive refinement procedure which is used for the solution of flow problems with a priori unknown local effects. For the parallel version of this procedure we showed the need for a dynamic load balancing. A global strategy for this balancing was described in detail. We presented results for the performance of this strategy and compared it with a local strategy. We showed the excellent convergence behaviour of our strategy and the usefulness of the dynamic load balancing together with the adaptive refinement. Dynamic load balancing is fully parallel and hardware independent, so that changes of the basic hardware nodes can be done without changing the developed algorithm. To exploit this advantage of our algorithms, they must be implemented in as portable a manner as possible. To achieve this, our further research will concentrate on porting the current implementation to mpi and studying the resulting performance on different hardware platforms. Reference