Focusing of Converging Cylindrical Shock Wave.

Shock wave focusing using geometrical shock dynamics

A finite-difference numerical method for geometrical shock dynamics has been developed based on the analogy between the nonlinear ray equations and the supersonic potential equation. The method has proven to be an efficient and inexpensive tool for approximately analyzing the focusing of weak shock waves, where complex nonlinear wave interactions occur over a large range of physical scales. The...

Periodic Wave Shock solutions of Burgers equations

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...

Converging cylindrical magnetohydrodynamic shock collapse onto a power-law-varying line current

W. Mostert1,†, D. I. Pullin2, R. Samtaney3 and V. Wheatley1 1School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD 4072, Australia 2Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, CA 91125, USA 3Mechanical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-690...

Converging cylindrical shocks in ideal magnetohydrodynamics

Numerical Solution of Cylindrically Converging Shock Waves

 Abstract—The cylindrically converging shock wave was numerically simulated by solving the Euler equations in cylindrical coordinates with TVD scheme and MUSCL [1] approach, using Roe's approximate Riemann solver [2] and super-bee nonlinear limiter [3]. The present study used the in house code developed for this purpose. The behavior of the solution in the vicinity of axis is investigated and ...