Numerical Treatment of Spherical Shock Waves

Abstract

The development of nuclear weapons heralded the need for numerical methods for predicting the hydrodynamic effects of these devices outside the very strong shock regime. The similarity solution to the intense point-source explosion in air only applies to the early phases of the explosion where the pressures generated are very much greater than the ambient air pressure. The blast wave becomes progressively weaker at later stages of the expansion and the pressure behind the shock front will eventually becomes comparable with the atmospheric pressure. The self-similar solution no longer applies when the pressure drops below about 20 atmospheres [1]. Consequently, it becomes necessary to take into account the counter-pressure which has so far been neglected and, when this is included, the partial differential equations describing the flow must be integrated numerically. Von Neumann, who provided an analytical solution to the point-source strong shock problem, [2] pioneered the application of numerical techniques for blast wave problems and was instrumental in the development of high-speed computing machines for performing numerical calculations.