Article information

2003 , Volume 8, Special issue, p.67-81

Kuropatenko V.F.

Methods of shock wave calculation

Certain manipulation with the mass, momentum and energy conservation laws, written in the form of partial differential equations for an ideal non-heat- conducting medium, give a corollary saying about entropy conservation along the particle trajectory. Conservation laws on the surface of a strong shock are algebraic equations showing that entropy grows across the shock wave. This is the fundamental difference between a shock wave and a continuous solution. We will discuss only the shock wave methods that treat the strong discontinuity as a layer of a finite width (the shock is smeared within an interval of a finite length called distraction) comparable with the size of the mesh cell. Since states behind and before the shock are related, then there must exist a mechanism that ensures the growth of entropy in the shock distraction region. Only four principally different mechanisms of energy dissipation in the distraction region are known [1-4]. Consider four shock wave methods corresponding to these four mechanisms. Many difference schemes can be used to implement them. I suggest that we look only at those that were proposed by the authors of these four methods [1-4]. B.L. Rozhdestvensky and N.N. Yanenko [5] were first to try to compare these methods, focusing on approximations and stability.

Classificator Msc2000:
*76-02 Research exposition (monographs, survey articles)
76L05 Shock waves and blast waves
76M99 None of the above, but in this section

Keywords: energy dissipation, approximation viscosity method, approximation error, mesh interval

Author(s):
Kuropatenko Valentin Fedorovich
Dr. , Professor
Position: General Scientist
Address: 456770, Russia, Snezhinsk
E-mail: v.f.kuropatenko@vniitf.ru


Bibliography link:
Kuropatenko V.F. Methods of shock wave calculation // Computational technologies. 2003. V. 8. The Special Issue: Proceedings of the Russian-German Advanced Research Workshop on Computer Science and High Performance Computing, Part 1. P. 67-81
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