Piston-driven converging shock wave in a stiff gas

The problem of a one-dimensional curvilinear shock wave converging into an ideal gas was first investigated by Guderley in 1942. Since then, many authors have discussed the practical notion of how Guderley-like flows might be generated. An obvious candidate is a ‘curvilinear piston,’ giving rise to a converging shock wave in the spirit of its planar counterpart. A limitation of existing analyses along these lines is the restriction to flows in materials described by an ideal gas equation of state (EOS) constitutive law. This choice is necessary for the direct comparison with the Guderley solution, which also features an ideal gas EOS. However, the ideal gas EOS is limited in its utility. The current work is thus intended to provide an extension of previous work to a non-ideal EOS. The stiff gas EOS is chosen as a logical starting point, due not only to its resemblance to the ideal gas law, but also its relevance to the shock compression of various liquid and solid materials. Given the stiff gas EOS is not otherwise expected to admit a Guderley-like solution when coupled to the inviscid Euler equations, this work provides the semi-analytical limiting behavior of a flow that cannot be otherwise captured using similarity analysis.