Algorithmic Trends in Computational Fluid Dynamics by Joseph L. Steger (auth.), M. Y. Hussaini, A. Kumar, M. D.

By Joseph L. Steger (auth.), M. Y. Hussaini, A. Kumar, M. D. Salas (eds.)

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SIAM J. Numer. Anal. 22,455-473, 1985. Scott, R. 1990. Zhang, S. Higher Dimensional Nonnested Multigrid methods. Research Report UH/MD-84. University of Houston. L. Fezoui: Numerical simulation of Euler equations on the Connection Machine. INRIA report 1990. R. F. Wheeler: Domain decomposition and Mixed Finite Element Methods for Elliptic Problems. In Domain Decomposition Methods for PDE . R. H. Golub, G. Meurant, J. Periaux eds. SIAM Philadelphi, p350-369 1988. 49 [26J F. Brezzi, C. Canuto, A.

The more sophisticated and efficient algorithms, those using block tridiagonal implicit procedures, will be more difficult or impossible to adapt. It will appear at first as a major step forward in hardware, a shift backwards in CFD software, and probably a net increase in computer resources. With time new algorithms that never could have been conceived of for use on serial computers will then hopefully evolve for the efficient use of massively parallel computer hardware. The major difficulties will be partitioning the computational problem to the multitude of processors, mapping both the grid and the algorithm to the processors with the goal of minimizing interprocessor communication.

Math Compo 50 , 181, p19-51, 1981. [6] C. Johnson, A. Szepessy: On the Convergence of a Finite Element Method for a Nonlinear Hyperbolic Conservation Law. Math. Compo 49 p427-444, 1987. [7] D. Serre: Oscillations non-lineaires hyperboliques de grandes amplitiudes. Internal report 33, ENS-Lyon, 1990. [8] A. Majda: Compressible Fluid Flow and Systems of Conservation Law in Several Space Variables. Springer series in Applied Mathematical Sciences 53 , 1984. [9] R. DiPerna: Measure-valued solutions to Conservation Laws.

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