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A multigrid acceleration technique developed for solving the three dimensional Navier-Stokes equations for subsonic/transonic flows has been extended to supersonic/hypersonic flows. An explicit multistage Runge Kutta type of time-stepping scheme is used as the basic algorithm in conjunction with the multigrid scheme. Solutions have been obtained for a blunt conical frustum at Mach 6 to demonstrate the applicability of the multigrid scheme to high speed flows. Computations have also been performed for a generic High-Speed Civil Transport configuration designed to cruise at Mach 3. These solutions demonstrate both the efficiency and accuracy of the present scheme for computing high-speed viscous flows over configurations of practical interest.

This study is concerned with viscous/inviscid interactions in two and quasi-three-dimensional supersonic flows with separation. Interaction effects are modeled through the so called 'displacement body concept', wherein it is assumed that the inviscid flow 'sees' an effective body obtained by adding the displacement thickness to the original surface. The governing equations in the viscous region are taken to be the interacting boundary-layer equations and an alternating-direction-implicit (ADI) finite difference scheme is employed to obtain their solution. This technique is applied to the quasi-three-dimensional problems resulting from flow past swept (yawed) and axisymmetric compression surfaces. Detailed distributions of surface pressure, skin friction and heat-transfer are presented for Mach numbers of 2 to 6. It is found that both cross flow and axisymmetric effects are easily accommodated in the solution technique and that the predicted results are in qualitative and quantitative agreement with available experimental data.

Contributions are made to finite Reynolds number, viscous/inviscid interaction theory for laminar, subsonic flow past a thin-airfoil trailing edge. In particular, an analytical/computational technique is developed for predicting high Reynolds number, attached or separated, trailing-edge and near-wake flow. The analysis is based on interacting boundary-layer theory in which the outer inviscid and the inner viscous flows are solved simultaneously to determine the complete flow past the displacement body. Inviscid solutions are based on linear airfoil theory and viscous solutions are determined by a finite difference approximation ot the boundary-layer equations cast in Levy-Lees variables. A semi-inverse viscous/inviscid iteration procedure is employed in which viscous and inviscid solutions are repeatedly determined until the inviscid pressure distribution at the displacement surface match the viscous pressure distribution., This article is from the Proceedings of the Symposium on Numerical and Physical Aspects of Aerodynamic Flows (2nd), 17-20 Jan 83, California State Univ. Long Beach, AD-A134 151.