Propogation of a curved weak shock

Journal of Fluid Mechanics

Volumn 434, Issue , 2001, Pages 119-151

  Monica, A ^a   Prasad, Phoolan ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELING; SHOCK WAVE; TWO-DIMENSIONAL FLOW; WAVE PROPAGATION;

EID: 0035837434     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112001003731     Document Type: Article

References (45)

1. ANILE, A. M., HUNTER, J. K., PANTANO, P. & RUSSO, G. 1993 Ray Methods for Nonlinear Waves in Fluids and Plasmas. Pitman.
2. ANILE, A. M. & RUSSO, G. 1986 Corrugation stability for plane relativistic shock waves. Phys. Fluids 29, 2847-2852.
3. BRIO, M. & HUNTER, J. K. 1992 Mach reflection for the two dimensional Burgers equation. Physica D 60, 194-207.
4. BRIO, M. & HUNTER, J. K. 1994 A von Neumann reflection for the 2-d Burgers equation. Proc. Symp. on Applied Mathematics, vol. 48, pp. 265-268.
5. CHOQUET-BRUHAT, Y. 1969 Ondes asymptotiques et approchees pour de systems d'equations aux derivées partialles nonlinéaires. J. Math Pures et Appl. 48, 117-158.
6. COCKBURN, B., SAN YIH-LIN & SHU, C. W. 1989 TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems. J. Comput. Phys. 84, 90-113.
7. COLLELA, P. & HENDERSON, L. F. 1990 The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213, 71-94.
8. GARDNER, C. S. & KRUSKAL, M. D. 1964 Stability of plane magnetohydrodynamic shocks. Phys. Fluids 7, 700-706.
9. GILES, M., PRASAD, P. & RAVINDRAN, R. 1996 Conservation form of equations of three dimensional front propagation. Preprint. Dept. Maths, Indian Institute of Science.
10. GLIMM, J. & LAX, P. D. 1970 Decay of solutions of nonlinear hyperbolic conservation laws. Am. Math. Soc. Memoir 101.
11. GRINFEL'D, M. A. 1978 Ray method for calculating the wave front intensity in nonlinear elastic material. J. Appl. Math. Mech. 42, 958-977.
12. HENSHAW, W. D., SMYTH, N. F. & SCHWENDEMAN, D. W. 1986 Numerical shock propagation using geometrical shock dynamics. J. Fluid Mech. 171, 519-545.
13. HUNTER, J. K. 1997 Nonlinear wave diffraction. In Geometrical Optics and Related Topics (ed. F. Colombini & N. Lerner), pp. 221-243. Birkhauser.
14. HUNTER, J. K. & BRIO, M. 2000 Weak shock reflection. J. Fluid Mech. 410, 235-261.
15. KEVLAHAN, N. K.-R. 1994 Structure and shocks in turbulence. PhD thesis, University of Cambridge.
16. KEVLAHAN, N. K.-R. 1996 The propagation of weak shocks in non-uniform flows. J. Fluid Mech. 327, 167-197.
17. LAZAREV, M. P., PRASAD, P. & SINGH, S. K. 1995 An approximate solution of one dimensional piston problem. Z. Angew. Math. Phys. 46, 752-771.
18. LEVEQUE, R. J. & YEE, H. C. 1990 A study of numerical methods for hyperbolic conservation laws with stiff source term. J. Comput. Phys. 86, 187-210.
19. MASLOV, V. P. 1980 Propagation of shock waves in an isentropic nonviscous gas. J. Soviet Maths 13, 119-163.
20. MONICA, A. 1999 Propagation of a curved weak shock front. PhD thesis, Indian Institute of Science, Bangalore.
21. MORTON, K. W., PRASAD, P. & RAVINDRAN, R. 1992 Conservation form of nonlinear ray equations. Tech. Rep. 2. Dept. of Maths, Indian Institute of Science.
22. PARKER, D. F. 1969 Nonlinearity, relaxation and diffusion in acoustics and ultrasonics. J. Fluid Mech. 39, 793-815.
23. PARKER, D. F. 1971 An asymptotic theory for oscillatory nonlinear signals. J. Inst. Maths Applics. 7, 92-110.
24. PRASAD, P. 1975 Approximation of perturbation equations in a quasilinear hyperbolic system in the neighbourhood of a bicharacteristic. J. Math Anal. Applics. 50, 470-482.
25. PRASAD, P. 1982 Kinematics of a multi-dimensional shock of arbitrary strength in an ideal gas. Acta Mech. 45, 163-176.
26. PRASAD, P. 1987 Extension of Huygen's construction of a wavefront to a nonlinear wavefront and a shock front. Current Sci. 56, 50-54.
27. PRASAD, P. 1993 Propagation of a Curved Shock and Nonlinear Ray Theory. Longman.
28. PRASAD, P. 1994 A nonlinear ray theory. Wave Motion 20, 21-31.
29. PRASAD, P. 1995 Formation and propagation of singularities on a nonlinear wavefront and a shock front. J. Indian Inst. Sci. 75, 517-535.
30. PRASAD, P. 2000 An asymptotic derivation of weakly nonlinear ray theory. Proc. Indian Acad. Sci. (Math. Sci.) 110, 1-17.
31. PRASAD, P. 2001 Nonlinear Hyperbolic Waves in Multi-dimensions. CRC Press.
32. PRASAD, P., RAVINDRAN, R. & SAU, A. 1991 On the characteristic rule for shocks. Appl. Math. Lett. 4, 5-8.
33. PRASAD, P. & SANGEETA, K. 1999 Numerical simulation of converging nonlinear wavefronts. J. Fluid Mech. 385, 1-20.
34. RAVINDRAN, R. & PRASAD, P. 1993 On an infinite system of compatibility conditions along a shock ray. Q. J. Appl. Maths Mech. 46, 131-140.
35. SCHWENDEMAN, D. W. 1988 Numerical shock propagation in non-uniform media. J. Fluid Mech. 188, 383-410.
36. SHU, C. W. 1987 TVB uniformly higher order schemes for conservation laws. Maths Comput. 49, 105-121.
37. SINGH, S. K. & SINGH, V. P. 1999 Approximate solution of 2-d piston problem. Z. Angew Math. Phys. 50, 1-16.
38. SRINIVASAN, R. & PRASAD, P. 1985 On the propagation of a multi-dimensional shock of arbitrary strength. Proc. Indian Acad. Sci. (Math. Sci.) 94, 27-42.
39. STRANG, G. 1968 On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5, 506-517.
40. STURTEVANT, B. & KULKARNI, V. A. 1976 The focusing of weak shock waves. J. Fluid Meth. 73, 651-671.
41. TABAK, E. G. & ROSALES, R. R. 1994 Focusing of weak shock waves and the von Neumann paradox of oblique shock reflection. Phys. Fluids 6, 1874-1892.
42. WHITHAM, G. B. 1956 On the propagation of weak shock waves. J. Fluid Mech. 1, 290-318.
43. WHITHAM, G. B. 1957 A new approach to problems of shock dynamics. Part 1. Two dimensional problems. J. Fluid Mech. 2, 145-171.
44. WHITHAM, G. B. 1959 A new approach to problems of shock dynamics. Part 2. Three dimensional problems. J. Fluid Mech. 5, 369-386.
45. WHITHAM, G. B. 1974 Linear and Nonlinear Wares. Wiley.