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An Analytic Description of Converging Shock Waves in a Gas with Variable Density

In the present paper, we considered the self-similar solution of the gasdynamic equations of strong converging cylindrical and spherical shock waves moving through an ideal gas with initial density varying as rw, where r is the distance from the axis (or centre) of symmetry and w is a constant. The flow behind the shock is assumed to be adiabatic. A study of the singular points of the differential equations leads to an analytic description of the flow and a simple determination of the similarity exponent which is in excellent agreement with the earlier values obtained by sophisticated analytic or numerical methods.