Unsteady relativistic shock-wave diffraction by cylinders and spheres

Abstract

The unsteady relativistic shock-wave diffraction patterns generated by a relativistic blast wave impinging on a circular cylinder and a sphere are numerically simulated using some high-resolution relativistic kinetic beam schemes in a general coordinate system for solving the relativistic Euler equations of gas dynamics. The diffraction patterns are followed through about 6 radii of travel of the incident shock past the body. The complete diffraction patterns, including regular reflection, transition from regular to Mach reflection, slip lines, and the complex shock-on-shock interaction at the wake region resulting from the Mach shocks collision behind the body are reported in detail. Computational results of several incident shock Mach numbers covering the near ultrarelativistic limit are studied. Various contours of flow properties including the Lorentz factor and velocity streamline plots are also presented to add a better understanding of the complex diffraction phenomena. The three-dimensional relieving effects of the sphere cases are evident and can be quantitatively evaluated as compared with the corresponding cylinder cases.