Numerical Analyses of Reflection and Diffraction of Weak Shock Wave by a Wedge at Attack Angle

Analytical solutions of the wave equation are presented for the reflection and the diffraction of a plane wave by a wedge at attack angle, and are compared with results of simulations for flow fields induced by weak shock waves. An algebraic procedure is proposed to generate grid systems fitting a wedge in which the grid is clustered near the apex of the wedge and the orthogonality holds on the wedge surface. This is an extension of conformal mapping and can simply produce grid systems for simulations. The explicit TVD method is applied to numerically solve the gasdynamic equation for the simulations. Comparisons between results of the simulations and the analytical solutions show that the analytical solutions of the wave equations can generally approximate the flow fields induced by reflection and diffraction of weak shock waves although deviations between the simulations and the analytical solutions are noticeable near the apex of the wedge.