A Numerical Scheme for Shock Propagation in Three Dimensions

A numerical scheme for shock propagation in three space dimensions is presented. The motion of the leading shock surface is calculated by using Whitham's theory of geometrical shock dynamics. The numerical scheme is used to examine the focusing of initially curved shock surfaces and the diffraction of shocks in a pipe with a 90° bend. Numerical and experimental results for the corresponding two-dimensional or axisymmetrical cases are used to compare with the new and more complicated three-dimensional results