A Newton/upwind method and numerical study of shock wave/boundary layer interactions

The objective of the paper is two-fold. First, an upwind/central differencing method for solving the steady Navier-Stokes equations is described. The symmetric line relation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical, and other computational results. Secondly, the shock wave/boundary layer interactions are studied numerically, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, it is found that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.