Some numerical analyses of flows with separation

Computational study of high Reynolds number flow with large separation is the most important problem now in computational aerodynamics. Some examples of recent results of studies of such flows are presented. The methods used are finite-difference methods and vortex methods. The first example is that of an incompressible flow past two cylinders computed by the finite-difference method based on a stream function-vorticity formulation of the Navier-Stokes equations. It is pointed out that special care must be taken to determine the boundary values of the stream function on the bodies when using this method. The second example is that of an incompressible flow past a circular cylinder at a critical Reynolds number computed by the MAC method using an improved upwind difference. The sharp drag reduction is first captured numerically by this computation. Third is an example of the simplest version of the new vortex methods without conformal mapping, which enables us to compute incompressible flows with large separation very easily and economically. The last example is of a transonic flow past an oscillating airfoil computed by the Beam-Warming scheme.