Geometrical Shock Dynamics in a Noble-Abel stiffened gas medium

Abstract

We derive the shock strength area rule for a Noble-Abel stiffened gas (NASG) equation of a state required in Whitham's geometrical shock dynamics approach to determine shock wave dynamics in dense gases, liquids and solids. An exact formulation requiring the solution of an ordinary differential equation is provided. Closed form solutions of various levels of approximations are also obtained as an expansion in shock wave strength. The leading order approximation recovers the geometrical acoustic limit, while higher order approximations account for the medium's compressibility. The exact shock strength area relation and the various order approximations are illustrated for shocks in liquid water. The simple closed form of the first order solution predicts the shock strength area rule up to shock pressures of approximately twice the stiffening pressure in water, i.e., approximately 1-2 GPa.