ABSTRACT
The study of hyperbolic system of equations and the associated problem of determining the motion of a shock of arbitrary strength has received considerable attention in the literature. The determination of the shock motion requires the calculation of the flow in the region behind the shock. If the shock is weak, Friedrich’s theory [55] offers a solution to this problem. Other methods by which the rise of entropy across the shock can be accounted for approximately have been given by Pillow [143], Meyer [124], and Lighthill [109]. Approximate analytical solutions to the problem of decay of a plane shock wave have been proposed by Ardavan-Rhad [6] and Sharma et. al [179]. Other methods which are generally employed for solving this problem in case of strong shock waves belong to the so-called shock expansion theory; the reader is referred to the work carried out by Sirovich and his co-workers ([33] and [187]). A simple rule proposed by Whitham [210], called the characteristic rule or the CCW approximation, determines the motion of a shock without explicitly calculating the flow behind for a large, though restricted class of problems, with good accuracy. Although these methods have been developed in an ad hoc manner, they yield remarkably accurate results; see for example, the papers on shock propagation problems involving diffraction [40], refraction [29], focusing ([71], [28]), and stability [161].
