A critical review of the numerical solution of Navier-Stokes equations

Abstract : The mathematical foundation and the various practical aspects of the numerical solution of gas dynamic equations are critically reviewed with emphasis on obtaining quantitatively accurate solutions for application in various engineering and sciences. Computational stability rate of convergence and accuracy (or error estimate) are discussed. The promises and problems of the 4th generation computers are outlined within this perspective. Computational stability shoud not be obtained at the sacrifice of the convergence rate to and the accuracy of the final solution. With accuracy in mind, the explicit algorithms are likely preferrable to the implicit ones. Strict conservation of the difference formulation is recommended and exemplified to avoid the accumulation of local truncation errors and to facilitate the estimate of the errors in a steady state solution. Illustrative examples are given including supersonic flows with shocks. (Author)

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