By P. Bastian (auth.), Siegfried Wagner (eds.)
Within the DFG -Schwerpunktprogramm "Stromungssimulation mit Hochleistungsrechnern" and in the actions of the French-German cooperation of CNRS and DFG a DFG symposium on "Computational Fluid Dynamics (CFD) on Parallel platforms" used to be equipped on the Institut fur Aerodynamik and Gasdynamik of the Stuttgart college, 9-10 December 1993. This symposium used to be attended by way of 37 scientists. The medical software consisted of 18 papers that thought of finite aspect, finite quantity and a step Taylor Galerkin set of rules for the numerical answer of the Euler and Navier-Stokes equations on hugely parallel pcs with MIMD and SIMD structure and on paintings station clusters. Incompressible and compressible, regular and unsteady flows have been thought of together with turbu lent combustion with complicated chemistry. dependent and unstructured grids have been used. excessive numerical potency was once tested by means of multiplicative, additive and multigrid equipment. Shared reminiscence, digital shared reminiscence and disbursed reminiscence structures have been investigated, occasionally in keeping with an automated grid partitioning approach. numerous tools for area decomposition have been investigated. the foremost aspect of those equipment is the answer of the inter face challenge as the matrix concerned may be block dense. Multilevel decomposition could be very effective utilizing multifrontal set of rules. The numerical tools contain particular and implicit schemes. within the latter case the procedure of equations is frequently solved by way of a Gauss -Seidel line re laxation technique.
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Extra info for Computational Fluid Dynamics on Parallel Systems: Proceedings of a CNRS-DFG Symposium in Stuttgart, December 9 and 10, 1993
Thus, in future, we will implement the combina- 46 tion method on an array-like network of workstations using the parallel communication structure discussed in this paper. REFERENCES  H. BUNGARTZ, An adaptive Poisson solver using hierarchical bases and sparse grids, in Proceedings of the IMACS International Symposium on Iterative Methods in Linear Algebra, P. de Groen and R. , Amsterdam, Elsevier, 1992.  --, Dunne Gitter und deren Anwendung bei der adaptiven Losung der dreidimensionalen Poisson-Gleichung, Dissertation, Institut fiir Informatik, TU Miinchen, 1992.
D} let Wi denote the computational time for cluster j. Due to basic properties of the time-parallel algorithm we have The head processors are calculating the extrapolated values while all other processors are idle. The master processor calculates the subdiagonal error estimator. Because the arithmetic work of part 1 (first column entries) dominates ~t 2 (extrapolation and error estimation) load balancing is not disturbed significantly. NUMERICAL RESULTS In this chapter the numerical results for two different test cases are presented reflecting the quality of the time-stepping algorithm.
The accuracy of the combined solution drops down for increasing numbers of time steps. Our first experiments give us the hope that the combination method will still work for turbulence simulation, too. PARALLELIZATION ASPECTS Now, we study the parallelization properties of the combination method for workstation networks. For reasons of simplicity, we concentrate on the case where all possible grids are used to compute a sparse grid solution U1,M,N' For this case, the best parallelization rate can be achieved.
Computational Fluid Dynamics on Parallel Systems: Proceedings of a CNRS-DFG Symposium in Stuttgart, December 9 and 10, 1993 by P. Bastian (auth.), Siegfried Wagner (eds.)