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Numerical Treatment of Plane Shocks

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

Abstract

The numerical solution of several examples of plane shock waves using artificial viscosity and their comparison with theoretical predictions is the dominant feature of this chapter. The Lagrangian form of the equations in plane geometry is derived and after a short introduction to finite difference representations of differential equations, the discrete form of the equations is presented. Numerical solutions involving plane shocks arising from piston motion are presented, discussed and compared with the predictions of the Rankine-Hugoniot equations of Chap.  3. Reflected shocks are also considered. Piston withdrawal from a tube that generates an expansion wave is also discussed and the numerical results are compared with the predictions based on the method of characteristics presented in Chap.  2. Finally, some numerical results arising from an analysis of the shock tube are presented and discussed.

Keywords

Artificial viscosity Shock waves Numerical solutions Lagrangian equations Finite difference equations Numerical examples of plane shocks Shock tube 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Seán Prunty
    • 1
  1. 1.BallincolligIreland

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