Detonation capturing for stiff combustion chemistry

References

• Fickett , W and Davis , W C . 1979 . Detonation , Berkeley, CA : University of California .
   Google Scholar
• Taki , S and Fujiwara , T . 1981 . “ Numerical simulation of triple shock behaviour of gaseous detonation ” . In 18th Symp. on Combustion , 1671 – 81 . Philadelphia, PA : Combustion Institute .
   Google Scholar
• Schoeffel , S U and Ebert , F . A numerical investigation of a reestablishment of a quenched gaseous detonation . Proc. 16th Int. Conf. on Shocktubes and Waves . Weinheim : VCH .
   Google Scholar
• Boris , J P and Oran , E S . 1987 . Numerical Simulation of Reactive Flow , Amsterdam : Elsevier .
   Google Scholar
• Bourlioux , A and Majda , A . 1992 . Theoretical and numerical structure for unstable two-dimensional detonations . Combust. Flame , 90 : 211 – 29 .
   Web of Science ®Google Scholar
• Quirk , J J and Short , M . Numerical investigation of pulsating detonations . Proc. 20th Int. Symp. on Shock Waves . Pasadena, CA. Vol. 2 , pp. 1125 – 30 . Singapore : World Scientific .
   Google Scholar
• Williams , F A . 1985 . Combustion Theory, The Fundamental Theory of Chemically Reacting Flow Systems , Redwood City, CA : Addison-Wesley .
   Google Scholar
• Strang , G . 1968 . On the construction and comparison of difference schemes . SIAM J. Num. Anal. , 5 : 506 – 17 .
   Web of Science ®Google Scholar
• Colella , P , Majda , A and Roytburd , V . 1986 . Theoretical and numerical structure for reacting shock waves . SIAM J. Sci. Stat. Comput. , 7 : 1059 – 80 .
   Web of Science ®Google Scholar
• Majda , A . 1981 . A qualitative model for dynamic combustion . SIAM J. Appl. Math. , 41 : 70 – 93 .
   Web of Science ®Google Scholar
• Fickett , W . 1980 . Detonation in miniature . Am. J. Phys. , 47 : 1050 – 9 .
   Web of Science ®Google Scholar
• Pember , R . 1993 . Numerical methods for hyperbolic conservation laws with stiff relaxation I. Spurious solutions . SIAM J. Appl. Math. , 53 : 1293 – 330 .
   Web of Science ®Google Scholar
• LeVeque , R J and Yee , H C . 1990 . A study of numerical methods for hyperbolic conservation laws with stiff source terms . J. Comput. Phys. , 86 : 187 – 210 .
   Web of Science ®Google Scholar
• Griffiths , D F , Stuart , A M and Yee , H C . 1992 . Numerical wave propagation in an advection equation with a nonlinear source term . SIAM J. Num. Anal. , 29 : 1244 – 60 .
   Web of Science ®Google Scholar
• Almgren , R F . 1991 . High-frequency acoustic waves in a reacting gas . SIAM J. Appl. Math. , 51 : 351 – 73 .
   Web of Science ®Google Scholar
• Dold , J W , Short , M , Clarke , J F and Nikiforakis , N . 1995 . Accumulating sequence of ignitions from a propagating pulse . Combust. Flame , 100 : 465 – 73 .
   Web of Science ®Google Scholar
• Nikiforakis , N and Clarke , J F . 1997 . Quasi-steady structures in the two dimensional initiation of detonations . Proc. R. Soc. A , 452
   Google Scholar
• Lax , P D . 1973 . Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , SIAM Regional Conference Series in Applied Mathematics 11 Philadelphia, PA : SIAM .
   Google Scholar
• Strehlow , R A . 1984 . Combustion Fundamentals , New York : McGraw-Hill .
   Google Scholar
• Courant , R and Friedrichs , K O . 1948 . Supersonic Flow and Shock Waves , New York : Wiley .
   Google Scholar
• Bourlioux , A , Majda , A and Roytburd , V . 1991 . Theoretical and numerical structure for unstable one-dimensional detonations . SIAM J. Appl. Math. , 51 : 303 – 43 .
   Web of Science ®Google Scholar
• Rosales , R R and Majda , A J . 1983 . Weakly nonlinear detonation waves . SIAM J. Appl. Math. , 43 : 1086 – 118 .
   Web of Science ®Google Scholar
• Klein , R . 1990 . “ On the dynamics of weakly curved detonations ” . In Dynamical Issues in Combustion Theory , IMA Volumes in Mathematics and its Applications 35 Edited by: Liñan , A and Williams , F A . Berlin : Springer .
   Google Scholar
• Fernandez , G and Larrouturou , B . 1989 . “ Hyperbolic schemes for multi-component Euler equations ” . In Nonlinear Hyperbolic Equations–Theory, Numerical Methods, and Applications , Edited by: Ballmann , J and Jeltsch , R . Vol. 24 , 128 Braunschweig : Vieweg .
   Google Scholar
• Einfeldt , B . 1988 . On Godunov-type methods for gas dynamics . SIAM J. Num. Anal. , 25 : 294 – 318 .
   Web of Science ®Google Scholar
• Sweby , P K . 1984 . High resolution schemes using flux limiters for hyperbolic conservation laws . SIAM J. Num. Anal. , 21 : 995 – 1011 .
   Web of Science ®Google Scholar
• Munz , C D . 1986 . “ On the comparison and construction of two-step schemes for the Euler equations ” . In Notes on Numerical Fluid Mechanics , Vol. 14 , Braunschweig : Vieweg .
   Google Scholar
• LeVeque , R J . 1990 . Numerical Methods for Conservation Laws , Boston, MA : Birkhäuser .
   Google Scholar
• Klein , R and Stewart , D S . 1993 . The relation between curvature, rate state dependence and detonation velocity . SIAM J. Appl. Math. , 53 : 1401 – 35 .
   Web of Science ®Google Scholar