Converging finite-strength shocks

The converging shock problem was first solved by Guderley and later by Landau and Stanyukovich for infinitely strong shocks in an ideal gas with spherical and cylindrical symmetry. This problem is solved herein for finite-strength shocks and a non-ideal-gas equation of state with an adiabatic bulk modulus of the type B_s= -v∂p ∂v|_s = (p +B) f(v), where B is a constant with the dimensions of pressure, and f(v) is an arbitrary function of the specific volume. Self-similar profiles of the particle velocity and thermodynamic variables are studied explicitly for two cases with constant specific heat at constant volume; the Tait-Kirkwood-Murnaghan equation, f(v) = constant, and the Walsh equation, f(v) = v/A, where A = constant. The first case reduces to the ideal gas when B = 0. In both cases the flow behind the shock front exhibits an unbalanced buoyant force instability at a critical Mach number which depends upon equation-of-state parameters.