On the accuracy of block implicit and operator-splitting algorithms in confined flame propagation problems

References

• Ramos , J.I. 1983 . Numerical studies of laminar flame propagation in spherical bombs . AIAA J , 21 : 415 – 422 .
   Google Scholar
• Ramos , J.I. 1983 . “ A numerical study of one-dimensional enclosed flames ” . In Numerical Properties and Methodologies in Heat Transfer , Edited by: Shih , T.M. 529 – 546 . Washington, D.C : Hemisphere Publishing .
   Google Scholar
• Ramos , J.I. 1983 . “ Numerical studies of one-dimensional unsteady flame propagation ” . In Scientific Computing: Applications of Mathematics and Computing to the Physical Sciences , Edited by: Stepleman , R. , Carver , M. , Peskin , R. , Ames , W.F. and Vichnevetsky , R. 291 – 299 . Amsterdam : North-Holland Publ .
   Google Scholar
• Ramos , J.I. . Ignition of confined gaseous mixtures by hot surfaces and hot wires . AIAA 21st Aerospace Sciences Meeting . Reno, Nevada AIAA Paper No. 83-0240
   Google Scholar
• Sirignano , W.A. 1973 . One-dimensional analysis of combustion in spark-ignition engines . Combust. Set Techno , 7 : 99 – 108 .
   Web of Science ®Google Scholar
• Bellan , J.R. and Sirignano , W.A. 1973 . A theory of flame development and nitric oxide formation in stratified charge internal combustion engines . Combust. Sci. Techno , 8 : 51 – 68 .
   Web of Science ®Google Scholar
• Bellan , J.R. and Sirignano , W.A. 1976 . Combustion and NO formation in a stratified-charge engine: A two-turbulent equations model . Combust. Sci. Techno , 12 : 75 – 104 .
   Web of Science ®Google Scholar
• Ramos , J.I. 1984 . On some accurate finite-difference methods for laminar flame calculations . Int. J. Num. Meth. Fluids , 4 : 915 – 930 .
   Web of Science ®Google Scholar
• Ramos , J.I. 1985 . Development and application of an adaptive finite element method to reaction-diffusion equations . Int. J. Num. Meth. Fluids , 5 : 13 – 23 .
   Google Scholar
• Otey , G.R. and Dwyer , H.A. 1979 . Numerical study of the interaction of fast chemistry and diffusion . AIAA J , 17 : 606 – 613 .
   Google Scholar
• Reitz , R.D. . Computation of laminar flame propagation using an explicitnumerical method . Eighteenth Symp. (Int.) Comb . pp. 433 – 442 . Pittsburgh, Pennsylvania : The Combustion Institute .
   Google Scholar
• Reitz , R.D. 1981 . A study of numerical methods for reaction-diffusion equations . SIAM J. Sci. Stat. Comp , 2 : 95 – 106 .
   Google Scholar
• Ramos , J.I. 1983 . A review of some numerical methods for reaction-diffusion equations . Math. Comp. Simul , XXV : 538 – 548 .
   Web of Science ®Google Scholar
• Ramos , J.I. 1985 . Numerical solution of reactive-diffusive systems. Part 1: Explicit methods . Int. J. Comp. Math , 18 : 43 – 65 .
   Web of Science ®Google Scholar
• Ramos , J.I. 1985 . Numerical solution of reactive-diffusive systems. Part 2: Methods of lines and implicit algorithms . Int. J. Comp. Math , 18 : 141 – 161 .
   Web of Science ®Google Scholar
• Ramos , J.I. 1986 . Numerical solution of reactive-diffusive systems. Part 3: Time linearization and operator-splitting techniques . Int. J. Comp. Math , 18 : 289 – 309 .
   Web of Science ®Google Scholar
• Saul'yev , V.K. 1964 . Integration of Equations of Parabolic Type by the Method of Nets , New York : Pergamon Press .
   Google Scholar
• Beam , R.M. and Warming , R.F. 1976 . An implicit finite-difference algorithm for hyperbolic equations in conservation-law form . J. Comp. Phys , 22 : 87 – 100 .
   Web of Science ®Google Scholar
• Beam , R.M. and Warming , R.F. 1978 . An implicit factored scheme for the compressible Navier-Stokes equations . AIAA J , 16 : 393 – 402 .
   Google Scholar
• Briley , W.R. and McDonald , H. 1977 . Solution of the multidimensional compressible Navier-Stokes equations by a generalized implicit method . J. Comp. Phys , 24 : 372 – 397 .
   Web of Science ®Google Scholar
• Briley , W.R. and McDonald , H. 1980 . On the structure and use of linearized block implicit methods . J. Comp. Phys , 34 : 54 – 73 .
   Google Scholar
• Yanenko , N.N. 1971 . The Method of Fractional Steps , New York : Springer-Verlag .
   Google Scholar