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A numerical method for a converging cylindrical shock

Published online by Cambridge University Press:  28 March 2006

R. B. Payne
R. B. Payne
Affiliation:
Computing Laboratory, University of Manchester
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Abstract

The finite difference method due to Lax (1954) is used to solve the equations of motion for a cylindrically symmetric flow of a compressible fluid. In particular, a converging cylindrical shock is found to increase in strength in agreement with the formula of Chisnell (1957). The artificial diffusion introduced by the method causes the pressure to remain finite at the axis, but a reflected diverging shock is obtained.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 2 , Issue 2 , March 1957 , pp. 185 - 200
Copyright
© 1957 Cambridge University Press

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References

Butler, D. S. 1954 Armaments Research Establishment Rep. no. 54/55.
Chisnell, R. F. 1957 J. Fluid Mech. 2 (in the press).
Guderley, G. 1942 Luftfarhtforschung 19, 302–312.
Kantrowitz, A. & Perry, R. W. 1951 J. Appl. Phys. 22, 878–886.
Lax, P. D. 1954 Comm. Pure Appl. Math. 7, 159–193.
Neumann, J. von & Richtmyer, R. D. 1950 J. Appl. Phys. 21, 232–237.