On the dynamics of a shock-bubble interaction

Journal of Fluid Mechanics

Volumn 318, Issue , 1996, Pages 129-163

  Quirk, James J ^a,b   Karni, S ^c,d  

^a NASA LANGLEY RESEARCH CENTER   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c NEW YORK UNIVERSITY   (United States)

^d TEMPLE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; FLOW INTERACTIONS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; SHOCK WAVES;

EULER EQUATIONS; MESH REFINEMENT ALGORITHM; SHOCK BUBBLE INTERACTION; SHOCK CAPTURING SCHEME;

BUBBLES (IN FLUIDS);

BUBBLES; INTERACTIONS; SHOCK WAVES;

EID: 0030184154     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096007069     Document Type: Article

References (47)

1. ABD-EL-FATTAH, A. M. & HENDERSON, L. F. 1978a Shock waves at a fast slow gas interface. J. Fluid Mech. 86, 15-32.
2. ABD-EL-FATTAH, A. M. & HENDERSON, L. F. 1978b Shock waves at a slow fast gas interface. J. Fluid Mech. 89, 79-95.
3. ABGRALL, R. 1988 Generalisation of the Roe scheme for the computation of mixture of perfect gases. La Recherche Aérospatiale 6, 31-43.
4. BELL, J., BERGER, M., SALTZMAN, J. & WELCOME, M. 1994 Three-dimensional adaptive mesh refinement for hyperbolic conservation laws. SIAM J. Sci. Comput. 15, 127-138.
5. BEN-DOR, G. & TAKAYAMA, K. 1985 Analytical prediction of the transition from Mach to regular reflection over cylindrical concave wedges. J. Fluid Mech. 158, 365-380.
6. BERGER, M. J. & COLELLA, P. 1989 Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 67-84.
7. BERGER, M. J. & OLIGER, J. 1984 Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53, 482-512.
8. CATHERASOO, C. J. & STURTEVANT, B. 1983 Shock dynamics in nonuniform media. J. Fluid Mech. 127, 539-561.
9. COLELLA, P., GLAZ, H. M. & FERGUSON, R. E. 1989 Multifluid algorithm for Eulerian finite difference methods. Manuscript (unpublished).
10. DRUMMOND, J. P. & GIVI, P. 1994 Suppression and enhancement of mixing in high-speed reacting flow fields. In Combustion in High Speed Flows (ed. J. Buckmaster, T. L. Jackson & A. Kumar), pp. 191-229. Kluwer.
11. GLIMM, J. & MCBRYAN, O. 1985 A computational Model for interfaces. Adv. Appl. Maths 6, 422-435.
12. GRAHAM, R. L. 1969 Bounds on certain multiprocessing anomalies. SIAM J. Appl. Maths 17, 416-429.
13. GROVE, J. W. & MENIKOFF, R. 1990 Anomalous reflection of a shock wave at a fluid interface. J. Fluid Mech. 219, 313-336.
14. HAAS, J.-F. & STURTEVANT, B. 1987 Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities. J. Fluid Mech. 181, 41-76.
15. HENDERSON, L. F., COLELLA, P. & PUCKETT, E. G. 1991 On the refraction of shock waves at a slow-fast gas interface. J. Fluid Mech. 224, 1-27.
16. HILLIER, R. 1991 Computation of shock wave diffraction at a ninety degrees convex edge. Shock Waves 1, 89-98.
17. Hou, T. Y. & LE FLOCH, PH. 1994 Why nonconservative schemes converge to wrong solutions: Error analysis. Math. Comput. 62, 497-530.
18. KARNI, S. 1992 Viscous shock profiles and primitive formulations. SIAM J. Numer. Anal. 29, 1592-1609.
19. KARNI, S. 1994 Multi-component flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 31-43.
20. KARNI, S. 1995 A level-set capturing scheme for compressible interfaces. In Numerical Methods for Wave Propagation Phenomena (ed. E. F. Toro). Kluwer.
21. LARROUTUROU, B. 1991 How to preserve the mass fractions positive when computing compressible multi-component flows. J. Comput. Phys. 95, 59-84.
22. LAX, P. D. 1954 Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commum. Pure Appl Maths 7, 159-163.
23. LAX, P. D. 1972 Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. SIAM Monograph Series.
24. LÖHNER, R., PICONE, J. M. & BORIS, J. P. 1988 Wave structure produced by shock propagation through a dense bubble gas. In Proc. 16th Intl Symp. on Shock Tubes and Waves, Aachen, Germany 1987, Weinheim, Germany, 1988. (ed. by H. Gronig), pp. 613-619. VCH, Weinheim.
25. MARBLE, F. E., HENDRICKS, G. J. & ZUKOSKI, E. E. 1987 Progress toward shock enhancement of supersonic combustion processes. AIAA Paper 87-1880.
26. MESHKOV, Y. Y. 1970 Instability of a shock wave accelerated interface between two gases. NASA Transl. TT F-13, 074 R.F.
27. NEUMANN, J. VON 1963 Collected Works, vol. 6. Pergamon Press.
28. PICONE, J. M. & BORIS, J. P. 1988 Vorticity generation by shock propagation through bubbles in a gas. J. Fluid Mech. 189, 23-51.
29. PUCKETT, E. G. & SALTZMAN, J. S. 1992 A 3-D adaptive mesh refinement algorithm for multi-material gas dynamics. Physica D 60, 84-104.
30. QUIRK, J. J. 1991 An adaptive mesh refinement algorithm for computational shock hydrodynamics. PhD Thesis, Cranfield Institute of Technology, UK.
31. QUIRK, J. J. 1994 A contribution to the great Riemann solver debate. Intl J. Numer. Meth. Fluids 18, 555-574.
32. QUIRK, J. J. 1996 A parallel adaptive mesh refinement algorithm for computational shock hydrodynamics. To appear in Appl. Numer. Maths.
33. RICHTMYER, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl Maths 23, 297-319.
34. ROE, P. L. 1982 Fluctuations and signals - A framework for numerical evolution problems. In Numerical Methods for Fluid Dynamics (ed. K. W. Morton & M. J. Baines), pp. 219-257. Academic.
35. RUPERT, V. 1992 Shock-interface interaction: current research on the Richtmyer-Meshkov problem. In Shock Waves, Proc. 18th Intl. Symp. on Shock Waves, Sendai, Japan 1991 (ed. K. Takayama), pp. 83-94. Springer.
36. SAMTANEY, R. & ZABUSKY, N. J. 1994 Circulation deposition on shock-accelerated planar and curved density-stratified interfaces: models and scaling laws. J. Fluid Mech. 269, 45-78.
37. SCHWENDEMAN, D. W. 1988 Numerical shock propagation in non-uniform media. J. Fluid Mech. 188, 383-410.
38. SHERCLIFF, J. A. 1977 Vector Fields, p. 276. Cambridge University Press.
39. STRANG, G. 1968 On the construction and comparison of finite-difference schemes. SIAM J. Numer. Anal. 5, 506-517.
40. TON, V. T., KARAGOZIAN, A. R., ENGQUIST, B. E. & OSHER, S. J. 1991. Numerical simulation of inviscid detonation waves with finite rate chemistry. Proc. Combustion Inst. 1991 Fall Meeting, UCLA, Paper WSS/C91-101, pp. 482-512.
41. VAN DYKE, M. 1982 An Album of Fluid Motion p. 148, The Parabolic Press, Stanford, California.
42. WANG, J. C. T. & WIDHOPF, G. F. 1990 Numerical simulation of blast flowfields using a high resolution TVD finite volume scheme. Computers & Fluids 18, 103-137.
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. 1958 On the propagation of shock waves through regions of non-uniform area or flow. J. Fluid Mech. 4 337-360.
45. YANG, J., KUBOTA, T. & ZUKOSKI, E. E. 1993 Applications of shock-induced mixing to supersonic combustion. AIAA J. 31, 854-862.
46. YANG, J., KUBOTA, T. & ZUKOSKI, E. E. 1994 A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity. J. Fluid Mech. 258, 217-244.
47. ZWAS, G. & ROSEMAN, J. 1973 The effect of nonlinear transformations on the computation of weak solutions. J. Comput. Phys. 12, 179-186.