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 structures" used to be prepared on the Institut fur Aerodynamik and Gasdynamik of the Stuttgart college, 9-10 December 1993. This symposium was once attended by means of 37 scientists. The medical software consisted of 18 papers that thought of finite point, finite quantity and a step Taylor Galerkin set of rules for the numerical resolution 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. established and unstructured grids have been used. excessive numerical potency was once confirmed through multiplicative, additive and multigrid equipment. Shared reminiscence, digital shared reminiscence and dispensed reminiscence structures have been investigated, every now and then according to an automated grid partitioning process. a number of tools for area decomposition have been investigated. the most important element of those equipment is the solution of the inter face challenge as the matrix concerned should be block dense. Multilevel decomposition should be very effective utilizing multifrontal set of rules. The numerical equipment comprise specific and implicit schemes. within the latter case the approach of equations is usually solved via a Gauss -Seidel line re laxation technique.
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Additional info for Computational Fluid Dynamics on Parallel Systems: Proceedings of a CNRS-DFG Symposium in Stuttgart, December 9 and 10, 1993
7). Thus, in the last modification we can reduce the communication cost and, thus, the total complexity down to O(h N ), witch is independent of the number of workstations A (for more details, see ). k-l Fig. 7 Pipelining of computing and communication. 4 II1II CRAYY-MP ~ 5200110 Fig. 8 Parallelization results on a workstation network and on vectorcomputers in MFlops. PARALLELIZATION RESULTS ON A NETWORK OF WORKSTATIONS In this section, we turn to the results of our numerical experiments. We consider a Poisson-type model problem with Dirichlet boundary conditions.
For that, we only use a subset of all possible grids for the combination method. This restriction is also necessary to fulfil the higher smoothness requirements of the combination method. Therefore, the meaning of p changes. e. up to the maximum of all possible grids to be combined). Note that we don't have to change formula (4). The factors kL' kM, kN are defined as in (5). These definitions lead to mesh widths in the different directions according to (3). Each solution U't,M,N for a certain p is defined now on grid Oi;M,N' Thus, we have to solve p .
V. E. approximation The main ingredients of the numerical method are the following: 27 Figure 1: Finite element mesh and control volume for a node i • the use of an approximate Rieman solver of Roe with 2nd order MUSCL interpolation  for integrating the Euler fluxes in the equations of the mean field, and a mass fluxes upwinding for the convective fluxes tin the equations of the turbulent quantities; • a special treatment of the boundary conditions in the discrete weak formulation using characteristic equations ; • the use of an implicit time integration, which consists of a first explicit step: follows by an implicit linearized Newton correction: A Ll(wn+1 - wn) = w· - wn with A = Id _ Llt 8F .