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have recently -•^presented finite-difference techniques for solving the laminar, incompressible boundary-layer equations for separated flow. In the reversed flow region, the difference scheme for the streamwise convection term is switched from a backward to a forward difference to account for the change in flow direction. Since the calculation proceeds from the upstream boundary, the use of a forward difference requires the solution at the next downstream station from the one being computed, and hence repeated streamwise iterations are required from separation through reattachement to obtain a converged solution. In many cases this global iteration procedure is unnecessary since the velocity in the reversed flow region is small, typically 5% or less of the freestream velocity. Consequently, neglect of the streamwise convection in the reversed flow region should have only a slight influence on the resulting solution. For example, Reyhner and FluggeLotz 3 demonstrated that by setting the convection term uu x in the x momentum equation equal to zero for u less than zero, a stable finite-difference solution of the boundary-layer equations could be obtained with the usual forward-marching procedure for a separated flow. Not only does this approximation eliminate the well-known instability encountered in solving the boundary-layer equations in a direction opposite to that of the local flow, but it also results in a substantial reduction in computer time and storage as compared to that required for a global iteration procedure.In the present Note a similar approximation to that of Reyhner and Flugge-Lotz 3 is made by neglecting the streamwise convection of vorticity in the reversed flow region. This approximation is incorporated into the inverse boundarylayer procedure (displacement thickness prescribed) developed previously by Carter. 2 The resulting forwardmarching procedure is shown to be a rapid and accurate technique for solving separated flows of limited extent. The equations are solved by the Crank-Nicolson scheme in which column iteration is used at each streamwise station since the finite-difference equations are nonlinear. Instabilities which were encountered in these column iterations were eliminated by introducing timelike terms in the finite-difference equations to provide both unconditional diagonal dominance and a column iterative scheme, found to be stable using the von Neumann stability analysis. This technique is general, and should be applicable to other implicit finite-difference schemes such as the ADI solution procedure for solving the Navier-Stokes equations. Diagonal dominance, as discussed by Keller 4 and in the recent paper by Hirsh and Rudy, 5 is a sufficient condition which insures that error growth will not occur in the solution of the tridiagonal equations with the Thomas algorithm. In some cases Reyhner and Flugge-Lotz, 3 and later Werle et al. 6 in a similar investigation, encountered an unexplained instability in the reverse flow region which they eliminated by introducing a positive art...

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