A note on numerical simulation of vortical structures in shock diffraction

Abstract

In numerical simulation of the Euler equations, the slipstream or shear layer that appears behind a diffracted shock wave may develop small discrete vortices using fine computational meshes. Similar phenomena were also observed in the simulation of a Mach reflection that is accompanied by a shear layer. However, these small vortices have never been observed in any shock-tube experiment, although the wave pattern and the shape of the main vortex agree very well with visualization results. Numerical solutions obtained with coarse grids may agree better with experimental photos than those with very fine grids because of the pollution of the small vortices. This note tries to investigate the effect of viscosity on the small vortices by comparing the solutions of the laminar Navier-Stokes equations and the $k-\epsilon$ turbulence model. It is found that the small vortices are still observed in the solution of the laminar Navier-Stokes equations, although they can be suppressed by using the turbulence model. Numerical and experimental factors that are responsible for the deviation of the laminar solutions from experimental results are discussed. The secondary vortex in shock diffraction is successfully simulated by solving the Navier-Stokes equations.