References
1. J. Von Neumann, R.D. Richtmyer, A method for the numerical calculation of hydrodynamic
shocks. J. Appl. Phys. 21, 232 (1950)
2. C.F. Sprague III, The Numerical Treatment of Simple Hydrodynamic Shocks Using the Von
Neumann-Richtmyer Method, LA-1912 Report (Los Alamos Scientific Laboratory of the University of California, Los Alamos, 1955)
3. Ya.B. Zel’dovich, Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic
Phenomena, (Dover Publications, Inc., Mineola, 2002), Chapter 1
4. J.D. Anderson Jr., Computational Fluid Dynamics: The Basics with Applications (McGrawHill, New York, 1995)
5. T.J. Chung, Computational Fluid Dynamics, 2nd edn. (Cambridge University Press, New York,
2010), Chapter 3
6. J.D. Ramshaw, Elements of Computational Fluid Dynamics (Imperial College Press, London,
2011)
7. K.W. Morton, D.F. Mayers, Numerical Solution of Partial Differential Equations (Cambridge
University Press, New York, 1994)
8. D. Mihalas, B. Weibel-Mihalas, Foundations of Radiation Hydrodynamics (Dover Publications
Inc., New York, 1999), p. 273
Fig. 4.70 Showing pressure profile at the instant of collision (t ¼ 4172Δt) and the profiles as the
reflected shocks move apart. The markers (39.2, 46.4 and 51.2) show the position of the piston at the
times indicated. For the numerical procedure the following parameters apply; γ ¼ 1.4, κ ¼ 1.5,
Δx ¼ 0.4 and Δt ¼ 0.04 (see text)
214
4 Numerical Treatment of Plane Shocks
1. J. Von Neumann, R.D. Richtmyer, A method for the numerical calculation of hydrodynamic
shocks. J. Appl. Phys. 21, 232 (1950)
2. C.F. Sprague III, The Numerical Treatment of Simple Hydrodynamic Shocks Using the Von
Neumann-Richtmyer Method, LA-1912 Report (Los Alamos Scientific Laboratory of the University of California, Los Alamos, 1955)
3. Ya.B. Zel’dovich, Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic
Phenomena, (Dover Publications, Inc., Mineola, 2002), Chapter 1
4. J.D. Anderson Jr., Computational Fluid Dynamics: The Basics with Applications (McGrawHill, New York, 1995)
5. T.J. Chung, Computational Fluid Dynamics, 2nd edn. (Cambridge University Press, New York,
2010), Chapter 3
6. J.D. Ramshaw, Elements of Computational Fluid Dynamics (Imperial College Press, London,
2011)
7. K.W. Morton, D.F. Mayers, Numerical Solution of Partial Differential Equations (Cambridge
University Press, New York, 1994)
8. D. Mihalas, B. Weibel-Mihalas, Foundations of Radiation Hydrodynamics (Dover Publications
Inc., New York, 1999), p. 273
Fig. 4.70 Showing pressure profile at the instant of collision (t ¼ 4172Δt) and the profiles as the
reflected shocks move apart. The markers (39.2, 46.4 and 51.2) show the position of the piston at the
times indicated. For the numerical procedure the following parameters apply; γ ¼ 1.4, κ ¼ 1.5,
Δx ¼ 0.4 and Δt ¼ 0.04 (see text)
214
4 Numerical Treatment of Plane Shocks