Finite-Difference Implementation of Inviscid Separated Flows with Infinitely-Long Cusp-Ended Stagnation Zone around Circular Cylinder

Abstract

The classical Helmholtz problem is applied for modelling and numerical investigation of inviscid cusp-ended separated flow around circular cylinder. Two coordinate systems are used: polar for initial calculations and parabolic as topologically most suited for infinite stagnation zone. Scaling by the shape of the unknown free line renders the problem to computational domain with fixed boundaries. Difference schemes and algorithm for Laplace equation and for Bernoulli integral are devised. A separated flow with drag coefficient $C_x=0$ like the so called ``critical'' flow is obtained. The pressure distribution on the surface of cylinder and the detachment point compares quantitatively very well with the predictions of the hodograph method.