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.
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Notes
- 1.
Partial derivatives are used here to indicate the changes in position and time of specific particles; nonetheless, it should be understood that these partial derivatives imply that we are in fact following the path taken by specific particles of fluid according to the Lagrangian description.
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Prunty, S. (2019). Numerical Treatment of Plane Shocks. In: Introduction to Simple Shock Waves in Air . Shock Wave and High Pressure Phenomena. Springer, Cham. https://doi.org/10.1007/978-3-030-02565-6_4
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DOI: https://doi.org/10.1007/978-3-030-02565-6_4
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