Numerical investigation of 3D shock focusing effects on the basis of the Euler equation

Abstract

In the present paper, we investigate the influence of the initial condition of a three-dimensional (3D) shock focusing problem on its solution. We search for an optimum combination of initial values to produce a maximum pressure amplification under the condition that the total energy input in the system is constant for each parameter combination. The flow problem consists of a spherical high-pressure gas volume, which is released at an initial time, t=0, within a cubical cavity with rigid walls. The developing shock wave is reflected on the walls and focuses in the centre of the cube, leading to a strong local increase of pressure and temperature. Optimum conditions can be found to reach a maximum amplification of pressure and temperature with constant energy input in the system. To investigate this flow problem, we use a Total Variational Diminishing-upwind method to solve the Euler equations of gas dynamics. The time integration is carried out explicitly by a multi-step method. The extension to three spatial dimensions is based on the Strang-type operator splitting. The implementation of the algorithm on a parallel computer (Fujitsu VPP-300/4) in the domain decomposition approach is discussed.