An implementation of the robust inviscid wall boundary condition in high-speed flow calculations

Boundary condition is one of the major factors to influence the numerical s tability and solution accuracy in numerical analysis. One of the most impor tant physical boundary conditions in the flowfield analysis is the wall bou ndary condition imposed on the body surface. To solve a two-dimensional Eul er equation, totally four numerical wall boundary conditions should be pres cribed. Two of them are supplied by the flow tangency condition. The other two conditions, therefore, should he prepared additionally in a suitable wa y. In this paper, four different sets of wall boundary conditions are propo sed and then applied to solve high-speed flowfields around a quarter circle geometry. A two-dimensional compressible Euler solver is prepared based on the finite volume method. This solver hires three different upwind schemes ; Steger-Warming's flux vector splitting, Roe's flux difference splitting, and Lieu's advection upstream splitting method. It is found that the way to specify the additional numerical wall boundary conditions strongly affects the overall stability and accuracy of the upwind schemes in high-speed flo w calculation. The optimal wall boundary conditions should be also chosen v ery carefully depending on the numerical schemes used to solve the problem.