Numerical Treatment of Spherical Shock Waves

  • Seán Prunty
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


The numerical treatment of very strong spherical shock waves is the subject matter of this chapter. The Lagrangian equations in normalized form with artificial viscosity included are presented for spherical symmetric flow while radial distances are normalized with respect to a length based on the total blast energy and ambient air pressure. Two specific numerical procedures are presented; one in relation to the point source explosion and the second in relation to the expansion of very hot high-pressure isothermal sphere into the surrounding atmosphere. In relation to the point source explosion, Taylor’s strong shock solution was taken as initial conditions with an initial pressure of 1000 atmospheres and the equations are numerically integrated over a time interval where the pressure at the shock front drops to just a few atmospheres. The isothermal sphere had a starting pressure of 1000 atmospheres and the numerical procedure was run over a time interval where the overpressure at the shock front was down to less than 0.2 atmospheres. Several plots of pressure, density and particle velocity are presented.


Spherical shock waves Lagrangian equations for spherical symmetric flow Artificial viscosity Point source solution Numerical solution Expansion of an isothermal sphere 


  1. 1.
    Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover Publications, Inc., Mineola, New York, 2002), Chapter 1Google Scholar
  2. 2.
    J. von Neumann, The Point Source Solution, Collected Works, vol 6 (Pergamon Press, New York, 1976), p. 219Google Scholar
  3. 3.
    H.L. Brode, Numerical Solutions of Spherical Blast Waves. J. Appl. Phys. 26, 766 (1955)MathSciNetCrossRefGoogle Scholar
  4. 4.
    H.L. Brode, The Blast from a Sphere of High Pressure Gas, Report No. P-582 (Rand Corporation, Santa Monica, California, January 1955)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Seán Prunty
    • 1
  1. 1.BallincolligIreland

Personalised recommendations