Wave refraction at an interface
Author:
C. M. Ablow
Journal:
Quart. Appl. Math. 18 (1960), 15-29
MSC:
Primary 76.45; Secondary 76.39
DOI:
https://doi.org/10.1090/qam/135022
MathSciNet review:
135022
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Abstract: A plane wave in one of two perfect gases moves toward the parallel plane interface between the gases. The wave is either continuous or headed by a shock front weak enough that entropy changes may be neglected. Using Riemann’s solution of the appropriate hyperbolic partial differential equation, four equations are derived giving the details of the reflected and refracted wave motions. The equations are of first order integro-differential or implicit functional form depending on the boundary conditions and must be solved simultaneously for four functions of a single independent variable. The equations are suitable for numerical step-by-step solution.
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W. E. Drummond, Explosive induced shock waves. Part I, Plane shock waves, J. Appl. Phys. 28, 1437-41 (1957)
R. Courant and K. O. Friedrichs, Supersonic flow and shock waves, Interscience Publishers, New York, 1948
R. Courant and D. Hilbert, Methoden der mathematischen Physik, Julius Springer, Berlin, 1937
W. E. Drummond, Interaction of nonuniform shock waves, J. Appl. Phys. 28, 76-85 (1957)
G. E. Duvall and B. J. Zwolinski, Entropic equations of state and their application to shock wave phenomena in solids, J. Acoust. Soc. Amer. 27, 1054-8 (1955)
F. D. Murnaghan, Finite deformation of an elastic solid, John Wiley and Sons, New York, 1951
D. C. Pack, The reflection and transmission of shock waves. I. The reflection of a detonation wave at a boundary; II. The effect of shock waves on an elastic target of finite thickness, Phil. Mag. (8) 2, 182-95 (1957)
J. M. Walsh and R. H. Christian, Equation of state of metals from shock wave measurements, Phys. Rev. (2) 97, 1544-56 (1955)
J. M. Walsh, R. G. Shreffler and F. J. Willig, Limiting conditions for jet formation in high velocity collisions, J. Appl. Phys. 24, 349-59 (1953)
C. Heinz, Reflexion ebener Druckwellen an einer festen Wand, Z. angew. Math. u. Mech. 37, 63-73 (1957)
W. E. Drummond, Explosive induced shock waves. Part I, Plane shock waves, J. Appl. Phys. 28, 1437-41 (1957)
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Article copyright:
© Copyright 1960
American Mathematical Society
