On the propagation of a weak shock front: Theory and application
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In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of “shock-rays”, which play the same role as the “rays” in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.
- Bryson, A. E., Gross, R. W. F.: Diffraction of strong shocks by cones, cylinders, and spheres. J. Fluid Mech.10, 1–16 (1961).
- Courant, R., Hilbert, D.: Methods of mathematical physics, Vol. 2. New York: Interscience 1962.
- Prasad, P.: Approximation of perturbation equations of a quasilinear hyperbolic system in the neighbourhood of a bicharacteristic. J. Math. Anal. and Appl.50, 470–482 (1975).
- Prasad, P.: Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas. Acta Mechanica45, 163–176 (1982).
- Sturtevant, B., Kulkarny, V. A.: The focusing of weak shock waves. J. Fluid Mech.73, 651–671 (1976).
- Whitham, G. B.: A new approach to shock dynamics, Part I: Two dimensional problems. J. Fluid Mech.2, 146–171 (1957).
- Whitham, G. B.: Linear and nonlinear waves. Wiley-Interscience Monographs 1974.
- On the propagation of a weak shock front: Theory and application
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