Accession Number : AD0717956

Title :   Numerical Solution of Quasi-Conservative Hyperbolic Systems - The Cylindrical Shock Problem,

Corporate Author : TEL-AVIV UNIV (ISRAEL) DEPT OF MATHEMATICAL SCIENCES

Personal Author(s) : Abarbanel,S. ; Goldberg,M.

Report Date : 26 JAN 1971

Pagination or Media Count : 54

Abstract : The paper discusses the numerical solution of hyperbolic systems of partial differential equations which are in quasi-conservation form. A basic Lax-Wendroff 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 C.F.L. (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 and the differences are pointed out. (Author)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), (*ITERATIONS, CONVERGENCE), (*SHOCK WAVES, HYDRODYNAMICS), EQUATIONS OF MOTION, COMPRESSIBLE FLOW, DIFFERENCE EQUATIONS, NUMERICAL ANALYSIS, ISRAEL

Subject Categories : Numerical Mathematics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE