Numerical simulation of flames as gas-dynamic discontinuities

REFERENCES

• Matalon , M. and Matkowsky , B. J. 1982 . Flames as gas-dynamic discontinuities . Journal of Fluid Mechanics , 124 : 239 – 259 . [CSA]
   Web of Science ®Google Scholar
• Matalon , M. , Cui , C. and Bechtold , J. K. 2003 . Hydrodynamic theory of premixed flames: Effects of stoichiometry, variable transport coefficients and arbitrary reaction orders . Journal of Fluid Mechanics , 487 : 179 – 210 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Pelce , P. and Clavin , P. 1982 . Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames . Journal of Fluid Mechanics , 124 : 219 – 237 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Frankel , M. L. and Sivashinsky , G. I. 1982 . The effect of viscosity on hydrodynamic stability of a plane flame front . Combustion Science and Technology , 29 : 207 – 224 . [CSA]
   Web of Science ®Google Scholar
• Matalon , M. and Matkowsky , B. J. 1984 . On the stability of plane and curved flames . SIAM Journal on Applied Mathematics , 44 : 327 – 343 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Bechtold , J. K. and Matalon , M. 1987 . Hydrodynamic and diffusion effects on the stability of spherically expanding flames . Combustion and Flame , 67 : 77 – 90 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Kim , Y. D. and Matalon , M. 1990 . On the stability of near-equidiffusional strained premixed flames . Combustion Science and Technology , 69 : 85 – 97 . [CSA]
   Web of Science ®Google Scholar
• Sivashinsky , G. I. 1977 . Nonlinear analysis of hydrodynamic instability in laminar flame – I. Derivation of basic equations . Acta Astronautica , 4 : 1177 – 1206 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Eteng , E. , Ludford , G. S.S. and Matalon , M. 1986 . Displacement effects of a flame in a stagnation-point flow . Physics of Fluids , 29 : 2172 – 2180 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Tien , J. H. and Matalon , M. 1992 . Effect of swirl on strained premixed flames for mixtures with Lewis number distinct from unity . Combustion Science and Technology , 87 : 257 – 273 . [CSA]
   Web of Science ®Google Scholar
• Huang , Z. , Bechtold , J. K. and Matalon , M. 1998 . Weakly stretched premixed flames in oscillatory flows . Combustion Theory and Modelling , 2 : 115 – 133 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Hirt , C. W. and Nichols , B. D. 1981 . Volume of fluid (VOF) method for the dynamics of free boundaries . Journal of Computational Physics , 39 : 201 – 225 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Osher , S. and Sethian , J. A. 1988 . Fronts propagating with curvature dependent speed: Algorithms based on Hamilton–Jacobi formulations . Journal of Computational Physics , 79 : 12 – 49 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Unverdi , S. O. and Tryggvason , G. 1992 . A front-tracking method for viscous incompressible, multi-fluid flows . Journal of Computational Physics , 100 : 25 – 37 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Yoo , S. and Stewart , D. S. 2005 . A hybrid level set method for modelling detonation and combustion problems in complex geometries . Combustion Theory and Modelling , 9 : 219 – 254 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Smiljanovski , V. , Moser , V. and Klein , R. 1997 . A capturing-tracking hybrid scheme for deflagration discontinuities . Combustion Theory and Modeling , 1 : 183 – 215 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Klein , R. 1999 . “ Numerics in combustion ” . In Introduction to Turbulent Combustion , Lecture Series 99-04 Edited by: Vervich , L. , Veynante , D. and Olivari , D. Rhode-Saint-Genese, , Belgium : von Karman Institute for Fluid Dynamics .
   Google Scholar
• Schmidt , H. and Klein , R. 2003 . A generalized level-set in-cell-reconstruction approach for accelerating turbulent premixed flames . Combustion Theory and Modeling , 7 : 243 – 267 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Qian , J. , Tryggvason , G. and Law , C. K. 1998 . A front tracking method for the motion of premixed flames . Journal of Computational Physics , 144 : 52 – 69 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Aldredge , R. C. and Zuo , B. 2001 . Flame acceleration associated with the Darrieus-Landau instability . Combustion and Flame , 127 : 2091 – 2101 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Pan , K. L. , Shyy , W. and Law , C. K. 2002 . An immersed-boundary method for the dynamics of premixed flames . Int. J. Heat Mass Trans. , 45 : 3503 – 3516 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Helenbrook , B. T. , Martinelli , L. and Law , C. K. 1999 . A numerical method for solving incompressible flow problems with a surface of discontinuity . Journal of Computational Physics , 148 : 366 – 396 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Nguyen , D. Q. , Fedkiw , R. P. and Kang , M. 2001 . A boundary condition capturing method for incompressible flame discontinuites . Journal of Computational Physics , 172 : 71 – 98 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wang , X. , Jackson , T. L. and Massa , L. 2004 . Numerical simulation of heterogeneous propellant combustion by a level set method . Combustion Theory and Modeling , 8 : 227 – 254 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Almgren , A. S. , Bell , J. B. and Szymczak , W. G. 1996 . A numerical method for the incompressible Navier–Stokes equations based on an approximate projection . SIAM Journal on Scientific Computing , 17 : 358 – 369 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Thual , O. , Frisch , U. and Henon , M. 1985 . Application of pole decomposition to an equation governing the dynamics of wrinkled flames . J. Physique , 46 : 1485 – 1494 . [CSA]
   Google Scholar
• Vaynblat , D. and Matalon , M. 2000 . Stability of pole solutions for planar propagating flames: I. Exact eigenvalues and eigenfunctions . SIAM Journal of Applied Mathematics , 60 : 679 – 701 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Vaynblat , D. and Matalon , M. 2000 . Stability of pole solutions for planar propagating flames: II. Properties of eigenvalues/eigenfunctions and implications to stability . SIAM Journal of Applied Mathematics , 60 : 702 – 728 . [CSA]
   Web of Science ®Google Scholar
• Peters , N. 2000 . Turbulent Combustion , Cambridge : Cambridge University Press .
   Google Scholar
• Darrieus , G. . Propagation d'un front de flamme . Unpublished paper presented at ‘Le congres de Mecanique Appliquee’ .
   Google Scholar
• Landau , L. D. 1944 . On the theory of slow combustion . Acta Physicochimica USSR , 19 : 77 [CSA]
   Google Scholar
• Markstein , G. H. 1964 . Nonsteady Flame Propagation , New York : Macmillan .
   Google Scholar
• Almgren , A. S. , Bell , J. B. , Colella , P. , Howell , L. H. and Welcome , M. L. 1998 . A conservative adaptive projection method for the variable density incompressible Navier–Stokes equations . Journal of Computational Physics , 142 : 1 – 46 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Sethian , J. A. 1996 . Level Set Methods and Fast Marching Methods , Cambridge : Cambridge University Press .
   Google Scholar
• Chopp , D. L. 2001 . Some improvements of the fast marching method . SIAM Journal of Scientific Computing , 23 : 230 – 244 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Peskin , C. S. 1977 . Numerical analysis of blood flow in the heart . Journal of Computational Physics , 25 : 220 – 252 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Michelson , D. M. and Sivashinsky , G. I. 1977 . Nonlinear analysis of hydrodynamic instability in laminar flames – II. Numerical experiments . Acta Astronautica , 4 : 1207 – 1221 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Gutman , S. and Sivashinsky , G. I. 1990 . The cellular nature of hydrodynamic flame instability . Physica D , 43 : 129 – 139 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Rahibe , O. , Aubry , N. and Sivashinsky , G. I. 1996 . Stability of pole solutions for planar propagating flames . Physical Review E , 54 : 4958 – 4972 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Rahibe , O. , Aubry , N. and Sivashinsky , G. I. 1998 . Intability of pole solutions for planar propagating flames in sufficiently large domains . Combustion Theory Modelling , 2 : 19 – 41 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar