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

ISBN-10: 1461227089

ISBN-13: 9781461227083

ISBN-10: 1461276381

ISBN-13: 9781461276388

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Finally we will discuss some recent problems that have arisen in conjunction with domain decomposition. 1. COMPRESSIBLE FLOW EQUATIONS: STATEMENT OF THE PROBLEM Existence results for large initial data is a very necessary prerequisite to numerical simulation of a system of Partial Differential Equations. Experience shows that much of the difficulties are solved once the existence problem is solved and convergence of numerical methods usually follows. G{W, V'W) = 0 (1) where W = {p, PUI, PU2, PU3, pEl and where G{W, V'W), F{W) are 5 x 5 matrices.

The viscosity depends on the meshsize we are willing (or better; forced by machine capacity) to use. Unfortunately, an efficient viscosity coefficient depends on the local "states". Although satisfactory ways to choose it have been found for particular problems, there is still no good theory to help in the choice. I am convinced that such a theory will be developed in the coming years. 2) Riemann solvers, method of characteristics. At the discontinuities the differential equations are replaced by algebraic conditions.

R. Sanders, A. Weiser: A high resolution Staggered Mesh Approach for Nonlinear Hyperbolic Systems of Conservation Laws. To appear in J. of Compo Physics, 1991. Y. Kuznetsov: Fictitious domain methods (to appear) Y. Achdou, O. Pironneau, R. Glowinski: Thning the mesh for a stream function vorticity formulation of the Navier-Stokes equations INRIA research report. Oct. 1991. D. J. Mavriplis: Three dimensional unstructured multigrid for the Euler equations. lease Report 91-41. 51 [54] L. Cowsar Parallel Domain Decomposition Method for Mixed FEM for Elliptic PDE.

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

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