Numerical Analyses of Reflection and Diffraction of Weak Shock Wave.

In order to investigate the accuracy of finite difference methods for weak shock waves, comparisons for the reflection and the diffraction of weak shock waves around wedges and corners between simulations and analyses are made. Analytical solutions are obtained for the wave equations by employing the conical flow method of Keller and Blank. Finite difference simulations are conducted by applying such finite difference methods as the total variation diminishing (TVD) method, the flux-corrected transport (FCT) method, the flux vector splitting (FVS) method and the method of Roe to numerically solve the Euler equations. Computed flow fields by the finite difference methods are almost equivalent to each other in the present investigation. The approximate solutions obtained from finite difference calculations deviate from the analytical exact solutions near the apexes of the wedges or the corners that are singular points in grid systems. The weaker the shock waves passing through the apexes, the more noticeable numerical errors originating from the singular points. Among the finite difference schemes examined in the present investigation, the TVD method is the most reliable because of its stability and smooth results. The FVS method is almost comparable to the TVD method. In the results of the FCT method, small noises are observed to be superposed. In the results of Roe's method, shock waves are simulated most sharply, but instabilities near the singular points are observed to be great.