The numerical simulations of explosion and implosion in air: Use of a modified Harten's TVD scheme

International Journal for Numerical Methods in Fluids

Volumn 31, Issue 4, 1999, Pages 661-680

  Liu, T G ^a   Khoo, B C ^a   Yeo, K S ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Radially symmetric flow; Second shock wave; TVD scheme

Indexed keywords

MATHEMATICAL MODELING; SHOCK WAVE;

EID: 0032712072     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/(sici)1097-0363(19991030)31:4<661::aid-fld866>3.0.co;2-g     Document Type: Article

References (22)

1. D.W. Boyer, 'An experimental study of the explosion generated by a pressurized sphere', J. Fluid Mech., 9, 401-429 (1960).
2. H.L. Brode, 'Theoretical solutions of spherical shock tube blasts', The RAND Corporation, RM-1974, 1957.
3. M.P. Friedman, 'A simplified analysis of spherical and cylindrical blast waves', J. Fluid Mech., 11, 1-15 (1961).
4. I.I. Glass, Nonstationary Flows and Shock Waves, Oxford Science Publications, Oxford, 1994.
5. W.E. Baker, Explosions in Air, Wilfred Baker Engineering, San Antonio, 1973.
6. J. Flores and M. Holt, 'Grimm's method applied to underwater explosions', J. Comput. Phys., 44, 377-387 (1981).
7. C. Shu, Private communication, Department of Mechanical Engineering, National University of Singapore, 1996.
8. P. Charrier and B. Tessieras, 'A front-tracking method applied to hyperbolic systems of nonlinear conservation laws', SIAM J. Numer. Anal., 23, 461-472 (1986).
9. J. Falcovitz and A. Birman, 'A singularities tracking conservation laws scheme for compressible duct flows', J. Comput. Phys., 115, 431-439 (1994).
10. M. Ben-Artzi and J. Falvovitz, 'A second-order Godunov-type scheme for compressible fluid dynamics', J. Comput. Phys., 55, 1-32 (1984).
11. G.A. Sod, 'A numerical study of a converging cylindrical shock', J. Fluid Mech., 83, 785-794 (1977).
12. A. Harten, 'High resolution schemes for hyperbolic conservation laws', J. Comput. Phys., 49, 357-393 (1983).
13. A. Harten, B. Engquist, S. Osher and S. Chakravarthy, 'Uniformly high-order-accurate essentially non-oscillatory scheme III', J. Comput. Phys., 71, 231-303 (1987).
14. C.W. Shu and S. Osher, 'Efficient implementation of essentially non-oscillatory shock-capturing schemes II', J. Comput. Phys., 83, 32-78 (1989).
15. A. Harten, 'The artificial compression method for computation of shocks and contact discontinuities: I. Single conservation laws', Comm. Pure Appl. Math., 30, 611-638 (1977).
16. A. Harten, 'ENO scheme with subcell resolution', J. Comput. Phys., 83, 148-384 (1989).
17. Mao De-Kang, 'A shock tracking technique based on conservation in one space dimension', SIAM J. Numer. Anal., 32, 1677-1703 (1995).
18. Huanan Yang, 'An artificial compression method for ENO schemes: the slope modification method', J. Comput. Phys., 89, 125-160 (1990).
19. A. Harten, 'The artificial compression method for computation of shocks and contact discontinuities: III. Self-adjusting hybrid schemes', Math. Comput., 32, 363-389 (1978).
20. S. Abarbanel and M. Goldberg, 'Numerical solution of quasi-conservative hyperbolic system - the cylindrical shock problem', J. Comput. Phys., 10, 1-33 (1972).
21. A. Lapidus, 'Computation of radially symmetric shocked flows', J. Comput. Phys., 8, 106-140 (1971).
22. R.B. Payne, 'A numerical method for a converging cylindrical shock', J. Fluid Mech., 2, 185-200 (1956).