The Computation of Steady Solutions to the Euler Equations: A Perspective

It is generally believed that the Navier-Stokes equations are necessary and sufficient for the description of laminar and turbulent flows. In the field of computational fluid dynamics (CFD), therefore, a major effort is made to develop accurate, robust and efficient computer codes for the numerical integration of these equations. The stimulus to this development comes in particular from the aerospace sciences, where the interest lies predominantly in predicting steady or almost steady flows. Most codes, therefore, do not aim at any temporal accuracy, thus making room for an extra computational effort to improve the spatial accuracy. This is no luxury, since the high-Reynolds-number flows studied with those codes exhibit very thin transition layers - boundary layers, vortex sheets and shock waves - separating the smoother regions. If these layers are not properly resolved on the adopted computational grid, numerical noise and even instabilities may arise, leading to losses of accuracy and efficiency. Finding the location of those layers is a problem of pattern recognition, the solution of which requires a fair share of the computational budget.

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