Numerical Analyses of Reflection and Diffraction of Weak Shock Waves.

Abstract

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. Among the finite difference schemes examined in the present investigation, the TVD method is the most reliable because of its stability and smooth resulting curves.