360 Veldman And

The paper describes the history of viscous-inviscid interaction methods, and tries to put them in a modern domain-decomposition context. This history started in 1904, when Ludwig Prandtl presented thèboundary layer' at the Third International Mathematical Congress in Heidelberg. From that moment on, the ow eld around a body was divided in two parts: a thin shear layer where viscosity plays a role, and the remaining outer part where the ow can be considered inviscid (Fig. 1). In the boundary layer the ow equations can be simpliied by neglecting the viscous streamwise derivatives, which changes the elliptic character of Navier-Stokes to a much easier handled parabolic character. The latter was very relevant in an era where mainly analytical tools were available for solving diierential equations. The boundary layer is driven by the external pressure distribution p e and (through Bernoulli's law) its related streamwise velocity u e. In the boundary layer the streamwise velocity component is reduced to zero, herewith eeectively thickening and smoothing the shape of the geometry. The resulting eeective shape is called the displacement body , which becomes a streamline for the inviscid ow.