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Shock Waves Stability and Perturbation Evolution


Study of Stability and Perturbation Evolution of Diverging and Converging Shock Waves

Tech Area / Field

  • PHY-NGD/Fluid Mechanics and Gas Dynamics/Physics

8 Project completed

Registration date

Completion date

Senior Project Manager
Zykov S A

Leading Institute
VNIIEF, Russia, N. Novgorod reg., Sarov


  • Lawrence Livermore National Laboratory, USA, CA, Livermore\nDefense Special Weapons Agency, USA, VA, Alexandria

Project summary

Theoretical study of perging and converging wave stability problem is planned in scope of the Project. The stability will be considered with respect to small non-radial axially symmetric perturbations. The perturbation evolution is planned to be studied using a method of direct computer simulation. Self-similar consideration will precede to the computer simulation. Self-similar results will serve the preliminary estimates for searching the cases of unstable blast wave 2D evolution.

The computer simulation will be carried out using the existing Hydrodynamic-with-Radiation 2D code based on the S.Godunov scheme.

The critical values of blast waves characteristics defining blast wave stability are planned to be calculated using the self-similar approach to the stability problem.

The further non-linear perturbation evolution is planned to be calculated for some unstable harmonics using computer simulation.

The following cases are planned to be considered:

- adiabatic point blast wave in an ideal gas.
- isothermal point blast wave in an ideal gas.
- point blast wave in an ideal gas in the case when an initial gas density is a power function of radius.
- self-similar converging shock wave in ideal gas, the primary shock wave.
- self-similar converging shock wave in ideal gas, the secondary (the reflected from the center) shock wave.

Also it is planned to prepare a survey about the evolution of perging and converging shock wave perturbations.

The approach that is suggested to study perturbation evolution was used earlier in /1/ It's efficiency was shown there. This approach includes the following parts:

1) Search of the adequate self-similar solutions that describe approximately perturbation evolution in the case considered. That is the entire problem solved earlier in 12/.
2) Direct computer simulation of 2-D blast wave using hydrodynamic code with the obtained self-similar solutions used as initial conditions for blast wave perturbations. Both mentioned above items are important.

1. V.M.Ktitoruv, V.Yu.Meltsas, report at the conference "Shock waves Instabilities", Si-Petersburg, June20-24, l996 (Published in Izvestija Vuzov)
2. V.M.Klitorov. Voprosy Atomnoi Nauki Tehniki, Ser.T.P.F, (Atomic Science and Technique Issues, Ser. Theor. Applied Phys.), N2 (2), 28 (1984);

Foreign collaborator of the Project:
Lewis A. Glenn
Head, Computation Physics Group
Department of Geophysics and Global Security
Lawrence Livermore National Laboratory,
Livermore, CA, US
Tel: 510-422-7239
FAX: 510-423-6907

Collaboration mode:

Discussion of results of the work on the Project using email exchanges of the results and occasional meetings in Russia and the U.S.


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