Weakly nonlinear and numerical analyses of dynamics in a solid combustion model

SIAM Journal on Applied Mathematics

Volumn 65, Issue 5, 2005, Pages 1708-1725

  Gross, L K ^a   Yu, J ^b  

^a University of Akron   (United States)

^b University of Vermont ^*  (United States)

Author keywords

Asymptotic expansions; Condensed phase combustion; Crank Nicolson method; Fourier transforms; Free boundary problems; Weak instability

Indexed keywords

ASYMPTOTIC EXPANSIONS; CONDENSED-PHASE COMBUSTION; CRANK-NICOLSON METHOD; FREE-BOUNDARY PROBLEMS; WEAK INSTABILITY;

ACTIVATION ENERGY; BOUNDARY CONDITIONS; COMBUSTION; COMPUTATIONAL METHODS; COMPUTER SIMULATION; FOURIER TRANSFORMS; MATHEMATICAL MODELS; NUMERICAL METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

NONLINEAR EQUATIONS;

EID: 27844579108     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139904439508     Document Type: Article

References (22)

1. A. BAYLISS AND B. J. MATKOWSKY, Two routes to chaos in condensed phase combustion, SIAM J. Appl. Math., 50 (1990), pp. 437-459.
2. A. F. BELYAEV AND L. D. KOMKOVA, Dependence of burning velocity of thermites on pressure, Zh. Fiz. Khim., 24 (1950), pp. 1302-1311.
3. M. R. BOOTY, S. B. MARGOLIS, AND B. J. MATKOWSKY, Interaction of pulsating and spinning waves in condensed phase combustion, SIAM J. Appl. Math., 46 (1986), pp. 801-843.
4. I. BRAILOVSKY AND G. SIVASHINSKY, Chaotic dynamics in solid fuel combustion, Phys. D, 65 (1993), pp. 191-198.
5. P. DIMITRIOU, J. PUSZINSKI, AND V. HLAVACEK, On the dynamics of equations describing gasless combustion, Combust. Sci. Tech., 68 (1989), pp. 101-111.
6. M. L. FRANKEL, L. K. GROSS, AND V. ROYTBURD, Thermo-kinetically controlled pattern selection, Interfaces Free Bound., 2 (2000), pp. 313-330.
7. M. L. FRANKEL AND V. ROYTBURD, Dynamical portrait of a model of thermal instability: Cascades, chaos, reversed cascades, and infinite period bifurcations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 4 (1994), pp. 579-593.
8. M. FRANKEL, V. ROYTBURD, AND G. SIVASHINSKY, A sequence of period doublings and chaotic pulsations in a free boundary problem modeling thermal instabilities, SIAM J. Appl. Math, 54 (1994), pp. 1101-1112.
9. M. L. FRANKEL, V. ROYTBURD, AND G. SIVASHINSKY, Complex dynamics generated by a sharp interface model of self-propagating high-temperature synthesis, Combust. Theory Model., 2 (1998), pp. 1-18.
10. M. GARBEY, H. G. KAPER, G. K. LEAF, AND B. J. MATKOWSKY, Quasi-periodic waves and the transfer of stability in condensed-phase surface combustion, SIAM J. Appl. Math., 52 (1992), pp. 384-395.
11. L. K. GROSS, Weakly Nonlinear Dynamics of Interface Propagation, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY, 1997.
12. L. K. GROSS, Weakly nonlinear dynamics of interface propagation, Stud. Appl. Math., 108 (2002), pp. 323-350.
13. S. B. MARGOLIS, Transition to nonsteady deflagration in gasless combustion, Progr. Energy Combust. Sci., 17 (1991), pp. 135-162.
14. B. J. MATKOWSKY AND G. I. SIVASHINSKY, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math., 35 (1978), pp. 465-478.
15. A. G. MERZHANOV, SHS processes: Combustion theory and practice, Arch. Combust., 1 (1981), pp. 23-48.
16. A. G. MERZHANOV, A. K. FILONENKO, AND I. P. BOROVINSKAYA, New phenomena in combustion of condensed systems, Soviet Phys. Dokl., 208 (1973), pp. 892-894.
17. Z. A. MUNIR AND U. ANSELMI-TAMBURINI, Self-propagating exothermic reactions: The synthesis of high-temperature materials by combustion, Mat. Sci. Rep., 3 (1989), pp. 277-365.
18. K. G. SHKADINSKY, B. I. KHAIKIN, AND A. G. MERZHANOV, Propagation of a pulsating exothermic reaction front in the condensed phase, Combust. Expl. Shock Waves, 7 (1971), pp. 15-22.
19. G. I. SIVASHINSKY, The structure of Bunsen flames, J. Chem. Phys., 62 (1975), pp. 638-643.
20. A. VARMA, A. S. ROGACHEV, A. S. MUKASYAN, AND S. HUANG, Combustion synthesis of advanced materials: Principles and applications, Adv. Chem. Engrg., 24 (1998), pp. 79-226.
21. J. YU AND L. K. GROSS, The onset of linear instabilities in a solid combustion model, Stud. Appl. Math., 107 (2001), pp. 81-101.
22. J. YU AND Y. YANG, Evolution of small periodic disturbances into roll waves in channel flow with internal dissipation, Stud. Appl. Math., 111 (2003), pp. 1-27.