Numerical solution of quasi-conservative hyperbolic systems—The cylindrical shock problem

Abstract

In this paper we consider the numerical solution of hyperbolic systems of partial differential equations which are in quasi-conservation form. A basic Lax-Wendrofl=like scheme is developed. In order to treat problems with discontinuous solutions an iterative procedure is proposed. The stability and convergence of the various schemes are investigated. It is shown that it is possible to have time steps considerably larger than those allowed according to the CFL (Courant-Friedricks-Levy) criterion. The method is then applied to the case of converging-diverging cylindrical shock waves. Detailed behavior near the axis at the time of shock coalescence is obtained, as well as the general flow field at various times. The results are compared with Payne [4] and the differences are pointed out. The computations reported herein were carried out on the CDC-3400 computer at the Tel-Aviv University computation center.