Numerical investigation of 3D shock focusing effects on the basis of the Euler equation

Computers and Fluids

Volumn 28, Issue 1, 1999, Pages 121-138

  Hartmann, Christoph ^a   Roesner, Karl G ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL FLUID DYNAMICS; EQUATIONS OF MOTION; FLOW OF FLUIDS; GAS DYNAMICS; INITIAL VALUE PROBLEMS; INTEGRATION; MATHEMATICAL OPERATORS; PARALLEL PROCESSING SYSTEMS; VARIATIONAL TECHNIQUES;

DOMAIN DECOMPOSITION METHOD; EULER EQUATION; SHOCK WAVE FOCUSING; TOTAL VARIATION DIMINISHING UPWIND METHOD;

SHOCK WAVES;

EULER FLOW; SHOCK WAVE;

EID: 0344177997     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7930(98)00021-8     Document Type: Book

References (36)

1. Apazidis N. Focusing of weak shock waves on a target in a parabolic chamber. Shock Waves. 3:1994;201-212.
2. Causon DM. On shock wave focusing in water with applications to extra-corporeal shock wave lithotripsy. Internal Report of Manchester Metropolitan University, private communications, 1995.
3. Chakravarthy SR et al. Application of a new class of high accuracy TVD schemes to the Navier-Stokes equations. AIAA 23rd Aerospace Sciences Meeting, 1985;AIAA 85-0165.
4. Einfeldt B, Munz C.D., Roe P.L., Sjörgreen B. On Godunov-type methods near low densities. J. Comput. Phys. 92:1989;273-295.
5. Glass I.I., Sharma S.P. Production of diamonds from graphite using explosive driven implosions. AIAA J. 14:1976;402-404.
6. Guderley G. Starke kugelige und zylindrische Verdichtungsstöße in der Nähe des Kugelmittelpunktes bzw. der Zylinderachse. Luftfahrtforschung. 42:1942;302-312.
7. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357-393.
8. Harten A, Lax P.D., van Leer B. On upstream differencing and Godunov-type-schemes for hyperbolic conservation laws. SIAM Rev. 25:1983;35-61.
9. Hartmann Chr, Roesner KG. Three-dimensional shock-focusing effects with an invariant difference scheme on a massively parallel computer. In: Proceedings of the 14th ICNMFD. Springer Lecture Notes in Physics, Springer, Berlin, 1995. p. 472-5.
10. Hartmann Chr, Roesner KG. Two-dimensional shock-focusing effects with a TVD-upwind-scheme on a massively parallel computer. In: Proceedings of the 3rd ICIAM, ZAMM. pp. 199-200, 1996.
11. Hartmann Chr, Roesner KG. Three-dimensional shock-focusing effects with a TVD-upwind-scheme on a massively parallel computer. In: Proceedings of the 6th ISCFD, 1995. p. 421-6.
12. Hwan-Seok Choi, Je-Hyun Baek. Computations of nonlinear wave interaction in shock-wave focusing process using finite volume TVD schemes. Comput. Fluids. 25:1996;509-525.
13. Hepp W, Grünewald M, Brendel W. Die extrakorporale Stoßwellen-Lithotripsie. Spektrum der Wissenschaft. 7:1991;44-53.
14. Hirsch Ch. Numerical computation of internal and external flows. New York: Wiley, 1990.
15. Inoue O, Takahashi N, Takayama K. Shock wave focusing in a log-spiral duct. AIAA J. 31:1993;1150-1153.
16. Inoue O, Imuta S, Milton B.E., Takayama K. Computational study of shock wave focusing in a log-spiral duct. Shock Waves. 5:1995;183-188.
17. Izumi K, Nakajima T, Aso S, Nishida M. Experimental and numerical studies of focusing process of weak shock waves. In: Memoirs of the Faculty of Engineering. Kyushu University, 1992.
18. Ho-Young Kwak, Hyup Yang. An aspect of sonoluminescence from hydrodynamics. J. Phys. Soc. Jap. 64:1995;1990-1992.
19. Leutloff D, Roesner K.G., Srivastava R.C., Kuwahara K. Numerical investigation of three-dimensional shock-focusing effects by an invariant difference scheme. Fluid Dynam. Res. 10:1992;469-482.
20. Leutloff D, Roesner K.G., Srivastava R.C. Numerical solution of converging shock problem. Comput. Fluids. 16:1988;175-182.
21. Liang S.M., Wu C.S., Yu F.M., Wu L.N. Numerical simulation of shock wave focusing over parabolic reflectors. Shock Waves. 5:1995;139-148.
22. Olivier H, Gronig H. The random choice method applied to two-dimensional shock-focusing and diffraction. J. Comput. Phys. 63:1986;85-106.
23. Payne R.B. A numerical method for a converging cylindrical shock. J. Fluid Mech. 2:1957;185-200.
24. Roe P.L. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43:1981;357-372.
25. Roe PL. Some contributions to the modelling of discontinuous flows. In: Proceedings of the AMS-SIAM Summer Seminar on Large Scale Computing in Fluid Mechanics. SIAM, Philadelphia, 1985. vol. 22.
26. Rusanov V.V. The calculation of non-stationary shock-waves with obstacles. USSR Comput Math Math Phys. 1:1962;304-320.
27. Sedov LI. Similarity and dimensional methods in mechanics. 10th ed. Boca Raton: CRC Press, 1993.
28. Sod G.A. A numerical study of a converging cylindrical shock. J Fluid Mech. 83:1977;785-794.
29. Sommerfeld M, Müuller H.M. Experimental and numerical studies of shock wave focusing in water. Experiments Fluids. 6:1988;209-216.
30. Strang G. On the construction and comparison of difference schemes. SIAM J Num Anal. 5:1968;506-517.
31. Takayama A, Kleine H, Grönig H. An experimental investigation of the stability of converging cylindrical shock waves in air. Experiments Fluids. 5:1987;315-322.
32. Takayama K. Application of underwater shock wave focusing to the development of extracorporeal shock wave lithotripsy. Jap J App Phys. Part 1:(32):1993;2192-2198.
33. van de Velde E. Concurrent scientific computing. Berlin: Springer, 1994.
34. Wu C.C., Roberts P.H. Shock-wave propagation in a sonoluminescing gas bubble. Phys Rev Lett. 70:1993;3424-3426.
35. Wu CC, Roberts PH. A model of sonoluminescence. In: Proceedings of the Royal Society London, A., 1994. vol. 445. p. 323-49.
36. Yee H.C. Construction of explicit and implicit symmetric TVD schemes and their applications. J Comput Phys. 68:1987;151-179.