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. O. , Pironneau, O. G. 1990. Numerical Analysis for Compressible Isothermal Flows. Proc. Symp. on Applied Math. Venice. Dervieux, A. 1985. Steady Euler simulations using unstructured meshes. Von Karman Lecture notes series 1884-04. , Johnson, C. 1988. An Adaptive Finite Element Method for Linear Elliptic Problems. Math Compo 50: 361383. L. Lions, B. Perthame, E. Tadmor: Kinetic formulation of scalar conservation laws. Note CRAS to appear. 1991. Y. Sone, K. Aoki, I.

I have discussed this issue with CFD developers and first line managers at two NASA laboratories, Langley Research Center and Ames Research Center, and find, unfortunately, that there is little agreement in narrowing the field concerning fu~ure directions in CFD. Perhaps it is because CFD is still a young discipline far from maturity itself and is to be implemented on computer architectures that are themselves still evolving and presently far from reaching a steady state. The direction of computer architecture today is toward massively parallel hardware systems.

T are not known, it is not obvious how to impose the boundary condition. In [17] convergence is shown (for the incompressible NavierStokes equations also) if one proceeds as follows. n. T = u x n is done through a given boundary integral in the formulation. T is know; all other integrals are approximated by Gauss quadratures. 42 Adaptation of this method to the compressible Navier-Stokes equations has not been done yet. It requires to take P and w as temporary variables even though they may be eliminated when the non linear system is built.

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