The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion

REFERENCES

• Carrier , G. F. , Fendell , F. E. , and Feldman , P. S. ( 1980 ). Dynamics of Reactive Systems , Academic Press , New York , pp. 333 – 352 .
   Google Scholar
• Chorin , A. J. ( 1980 ). Flame advection and propagation algorithms . Journal of Computational Physics 35 , 1 .
   Web of Science ®Google Scholar
• Chorin , A. J. ( 1973 ). Numerical studies of slightly viscous flow . Journal of Fluid Mechanics 57 , 785
   Web of Science ®Google Scholar
• Chorin , A. J. , and Marsden , J. ( 1979 ). A Mathematical Introduction to Fluid Mechanics , Springer. Verlag , New York .
   Google Scholar
• Embid , P. ( 1984 ). The equations or zero mach number combustion . Ph.D. thesis , U.C. Berkeley ( to appear ).
   Google Scholar
• Gelfand , M. , and Shilov , G. E. ( 1964 ). Generalized Functions , Vol. 1 , Academic Press , New–York .
   Google Scholar
• Ghoniem , A. F. , Chorin , A. J. , and Oppenheim , A. K. ( 1981 ). Numerical modelling of turbulent flow in a combustion tunnel . Philos. Trans. Roy. Soc. London, Sr. A , 1103 .
   Google Scholar
• van Harten , A. , and Matkowsky , B. J. ( 1982 ). A new model in flame theory . SIAMJ. Appl. Math. 42 , 850 .
   Web of Science ®Google Scholar
• Klainerman , S. , and Majda , A. ( 1982 ). Compressible and incompressible fluids . Comm. Pure Appl. Math. 35 , 629 .
   Web of Science ®Google Scholar
• Kurylo , J. , Dwyer , H. A. , and Oppenheim , A. K. ( 1980 ). Numerical analysis of flow fields generated by accelerated flames . A1AA J. 18 , 302 .
   Google Scholar
• Landau , L. D. ( 1944 ). On the theory of slow combustion . J. Exp. Theor. Phys. 14 , 240 .
   Google Scholar
• Majda , A. ( 1982 ). Equations of low Mach number combustion. Center for Pure and Applied Mathematics , University of Calfornia , Berkeley , Report No. 112 .
   Google Scholar
• Matkowsky , B. J. , and Sivashinsky , G. I. ( 1979 ). An asymptotic derivation of two models in flame theory associated with the constant density approximation . SI AM J. Appl Math. 37 , 686 .
   Web of Science ®Google Scholar
• Noh , W. T. , and Woodward , P. ( 1976 ). SLIC (Simple Line Interface Calculation) . Proc. 5th Int. Conf. Number. Math. Fluid Mechanics , Springer–Verlag , Berlin , p. 330 .
   Google Scholar
• Rehm , R. G. , and Baum , H. R. ( 1978 ). The equations of motion for thermally driven, boyuant flows . N.B.S. J. Res. 83 , 297 .
   PubMedGoogle Scholar
• Sethian , J. A. ( 1982 ). An analysis of flame propagation . Ph.D. Dissertation , University of California , Berkeley .
   Google Scholar
• Sethian , J. A. ( 1983a ). Numerical simulation of flame propagation in a closed vessel . Proc. Fifth Int. GAMM Conf. Numer. Meth. Fluid Mechanics , Rome , Italy .
   Google Scholar
• Sethian , J. A. ( 1984 ). Turbulent combustion in open and closed vessels . J. Comput. Phys. 55 .
   Web of Science ®Google Scholar
• Sethian , J. A. ( 1983b ). The wrinkling of a flame due to viscosity . In Ouintiere, J. (Ed.) , Fire Dynamics and Heat Transfer, Proc. 21st Nat. Heat Transfer Conf , p. 29 .
   Google Scholar
• Sivashinsky , G. I. ( 1979 ). Hydrodynamic theory of flame propagation in an enclosed volume . Acta Astronautica 6 , 631 .
   Web of Science ®Google Scholar
• Teman , R. ( 1977 ). The Naoier-Stokes Equations ( North Holland Press , Amsterdam ).
   Google Scholar
• Williams , F. A. ( 1964 ). Combustion Theory , Addison–Wesley , Reading , MA .
   Google Scholar