Analysis of strongly nonlinear blast waves using the Rankine-Hugoniot relations and the nonlinear ray theory

Abstract

Blast waves produced by such events as nuclear explosions can be considered as strongly-nonlinear shock waves, the description of which requires a theoretical framework more accurate than the second-order wave equation. In this regard, computational fluid dynamics (CFD) techniques based on the Euler equation are frequently used. However, CFD techniques are very time-consuming for blast waves traveling over great distances. This paper presents a theoretical framework for propagation of strongly nonlinear blast waves, which shines in both speed and accuracy. Local propagation speeds of a blast wave are obtained by applying the Rankine-Hugoniot relations to “infinitesimal shocks” between adjacent phase points comprising the blast wave. By grafting the propagation speed onto the nonlinear ray theory, the evolution of the blast wave can be computed. Phenomena characteristic of strongly-nonlinear blast waves such as the Mach reflection, the Mach stem generation, and the self-refraction are observed from numerical simulations.