suddenly released into the atmosphere. They solved this problem numerically by
using the method of characteristics. Besides the main outwardly moving shock, they
also established the existence of an inward travelling second shock. The method of
characteristics provides accurate treatment of shock discontinuities with well defined
boundaries in contrast to numerical methods using artificial viscosity where the
surface of discontinuity is spread out over several mesh intervals so that there is a
general lack of accuracy in determining the precise location of the shock surface. As
the details of their numerical technique are outside the scope of the present text, the
interested reader can obtain additional information in relation to the implementation
of their numerical technique in other reports [7, 8] by these authors.
References
1. Ya. B. Zel’dovich, Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic
Phenomena, (Dover Publications, Inc., Mineola, New York, 2002), Chapter 1
2. J. von Neumann, The Point Source Solution, Collected Works, vol 6 (Pergamon Press,
New York, 1976), p. 219
3. H.L. Brode, Numerical solutions of spherical blast waves. J. Appl. Phys. 26, 766 (1955)
4. H. L. Brode, The Blast from a Sphere of High-Pressure Gas, Report No. P-582, (Rand Corporation, Santa Monica, California, January 1955)
5. H. L. Brode, The Blast Wave in Air Resulting from a High-Temperature, High-Pressure Sphere
of Air, Report No. RM-1825-AEC, (Rand Corporation, Santa Monica, California, December
1956)
6. P.C. Chou, S.L. Huang, Late-stage equivalence in spherical blasts as calculated by the method of
characteristics. J. Appl. Phys. 40, 752 (1969)
7. S. L. Huang, P. C. Chou, Solution of blast waves by a constant time scheme in the method of
characteristics, Report No. 125-9 (Drexel Institute of Technology, Philadelphia, Pennsylvania,
August 1966)
8. S. L. Huang, P. C. Chou, Calculations of expanding shock waves and late-stage equivalence,
Report No. 125-12 (Drexel Institute of Technology, Philadelphia, Pennsylvania, April 1968)
312
6 Numerical Treatment of Spherical Shock Waves
using the method of characteristics. Besides the main outwardly moving shock, they
also established the existence of an inward travelling second shock. The method of
characteristics provides accurate treatment of shock discontinuities with well defined
boundaries in contrast to numerical methods using artificial viscosity where the
surface of discontinuity is spread out over several mesh intervals so that there is a
general lack of accuracy in determining the precise location of the shock surface. As
the details of their numerical technique are outside the scope of the present text, the
interested reader can obtain additional information in relation to the implementation
of their numerical technique in other reports [7, 8] by these authors.
References
1. Ya. B. Zel’dovich, Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic
Phenomena, (Dover Publications, Inc., Mineola, New York, 2002), Chapter 1
2. J. von Neumann, The Point Source Solution, Collected Works, vol 6 (Pergamon Press,
New York, 1976), p. 219
3. H.L. Brode, Numerical solutions of spherical blast waves. J. Appl. Phys. 26, 766 (1955)
4. H. L. Brode, The Blast from a Sphere of High-Pressure Gas, Report No. P-582, (Rand Corporation, Santa Monica, California, January 1955)
5. H. L. Brode, The Blast Wave in Air Resulting from a High-Temperature, High-Pressure Sphere
of Air, Report No. RM-1825-AEC, (Rand Corporation, Santa Monica, California, December
1956)
6. P.C. Chou, S.L. Huang, Late-stage equivalence in spherical blasts as calculated by the method of
characteristics. J. Appl. Phys. 40, 752 (1969)
7. S. L. Huang, P. C. Chou, Solution of blast waves by a constant time scheme in the method of
characteristics, Report No. 125-9 (Drexel Institute of Technology, Philadelphia, Pennsylvania,
August 1966)
8. S. L. Huang, P. C. Chou, Calculations of expanding shock waves and late-stage equivalence,
Report No. 125-12 (Drexel Institute of Technology, Philadelphia, Pennsylvania, April 1968)
312
6 Numerical Treatment of Spherical Shock Waves