Numerical simulation on the shock focusing mechanism using T.V.D. scheme

Abstract

The shock focusing phenomenon occurs when the shock wave enters into the inhomogeneous media, thereby producing high pressure or density. In this case the very effective numerical algorithm is highly desirable. The algorithm called T.V. D. (Total Variation Diminishing) has the basic principle of discrete or numerical conservation. The object of this paper is to consider the effects of the geometry, Mach number, and shock strength on the shock focusing mechanism. We have also showed the behaviors of the pressure, density, and flowfields behind the shock focusing. furthermore we have extended the T.V.D. scheme based on the modified flux method and the characteristic flux difference splitting method to the axisymmetric case the shock focusing mechanism over the concave wall could be well simulated by the above T.V.D scheme, and the validity of the T.V.D scheme to the axisymmetric case was verified by the comparison with experimental results.