2012 , Volume 17, № 1, p.3-16

The paper sets out from the inclusion of the analysis of existence and regularity of solutions of the Navier — Stokes equations in the seven unsolved problems of mathematics by the Clay Mathematics Institute in the USA in 2000. It then mentions d'Alembert's early paradoxical attempts to determine the aerodynamic drag and the insolvability of the Euler equations at the time when they were first published. After the discussion of the derivation of the Navier — Stokes equations early results as for example Helmholtz's vorticity theorems and Reynolds' approach to turbulent flows are introduced, followed by Prandtl's revolutionary boundary-layer theory and liftingline theory. The next section sketches the rapid development of modern computing machines, enabling the introduction of numerical methods into fluid mechanics. Arrangement of computational grids and solution techniques are briefly discussed. The results of a recent international workshop on drag prediction and an example showing the use of numerical methods in aerodynamic design are used to demonstrate the state of the art. The summary concludes with a look on future problems.