A Finite Volume Scheme on Unstructured Grids for Stiff Chemically Reacting Flows

References

• Bird , R. B. , Stewart , W. E and Lightfoot , E. N , ( 1960 ) Transport Phenomena , Wiley , New York .
   Google Scholar
• Bischof , C. , Carle , A. , Khademi , P. , Mauer , A. , and Hovland , P. ( 1995 ) ADIFOR 2,0 User's Guide. . Center for Research on Parallel Computation , Argonne National Laboratory , Technical Report CRPC-95516-S ,
   Google Scholar
• Chen , K. H. , Shuen , J. S. , and Choi , Y. ( 1992 ) A Time-Accurate Algorithm for Chemical NonEquilibrium Viscous Flows at All Speeds , AIAA Paper 92-3693 .
   Google Scholar
• Cheng , L. and Armfield , S. , ( 1995 ) A Simplified Marker and Cell Method for Unsteady Flows on Non-Staggered Grids . International Journal for Numerical Methods in Fluids , 21 , 15 – 34 .
   Web of Science ®Google Scholar
• Choi , D. , and Merkle , C L. ( 1985 ) Application of Time-Iterative Schemes to Incompressible Flow , AIAA Journal , 23 , 1518 – 1524 .
   Google Scholar
• Choi , Y. H. , and Merkle , C. L. ( 1993 ) The Application of Preconditioning in Viscous Flows , Journal of Computational Physics , lO5 , 207 – 223 .
   Google Scholar
• Chorin , A. J. ( 1967 ) A Numerical Method for Solving Incompressible Viscous Flow Problems , Journal of Computational Physics , 2 , 12 – 26 .
   Google Scholar
• Deuflhard , P. ( 1983 ) Order and Stepsize Control in Extrapolation Methods , Numerische Mathematik , 41 , 399 – 422 .
   Web of Science ®Google Scholar
• Deuflhard , P. and Nowak , U. ( 1987 ) Extrapolation Integrators for Quasilinear Implicit ODE , In Deuflhard , P. and Enquist , B. (Eds.), Large Scale Scientific Computing, Progress in Scientific Computing , Vol. 7 , 37 .
   Google Scholar
• Deuflhard , P. , Hairer , E. and Zugck , J. ( 1987 ) One-Step and Extrapolation Methods for Differential Algebraic Systems , Numerische Mathematik , 51 , 501 – 516 .
   Web of Science ®Google Scholar
• Deutschmann , O. , Riedel , U. and Warnatz , J. ( 1995 ) Modeling of Nitrogen and Oxygen Recombination on Partial Catalytic Surfaces . Journal of Heal Transfer (Transactions of the ASME) , 117 , 495 – 501 .
   Google Scholar
• Dick , E. ( 1988 ) A Flux-Vector Splitting Method for Steady Navier-Stokes Equations . International Journal for Numerical Methods in Fluids , 8 , 317 – 326 .
   Google Scholar
• Dwyer , H. A. ( 1994 ) Navier-Stokes Calculations of Multi-Dimensional Flows with Complex Chemical Kinetics , Computing Systems in Engineering , 5 , 105 – 116 .
   Google Scholar
• Flamm , D. L. , Donnelly , V. M. , and Mucha , J. A. , ( 1981 ) The Reactions of Fluorine Atoms with Silicon . Journal of Applied Physics , 52 , 3633 – 3639 .
   Web of Science ®Google Scholar
• Hirschfelder , J. O. , Bird , R. B. and Curtiss , C. F. , ( 1964 ) Molecular Theory of Gases and Liquids , Wiley , New York .
   Google Scholar
• Horibata , Y. ( 1992 ) Numerical Simulation of a Low-Mach-Number Flow with a Large Temperature Variation . Computers & Fluids , 21 , 185 – 200 .
   Web of Science ®Google Scholar
• Maas , U. and Warnatz , J. ( 1989a ) Simulation of Chemically Reacting Flows in Two Dimensional Geometries . Impact of Computing in Science and Engineering , 1 , 394 – 420 .
   Google Scholar
• Maas , U. and Warnatz , J. ( 1989b ) Simulation of Thermal Ignition Processes in Two Dimensional Geometries . Zeitschrift fio Physikalische Chemie, Neue Folge , 161 , 61 – 81 .
   Google Scholar
• Mack , A. , Weber , H. J. and Roth , P. ( 1991 ) A Moving Grid Method Applied to One-Dimensional Non-Stationary Flame Propagation . International Journal for Numerical Methods in Fluids , 13 , 869 – 882 .
   Web of Science ®Google Scholar
• Marx , Y. P. ( 1991 ) Evaluation of the Artificial Compressibility Method for the Solution of the lmcompressible Navier-Stokes Equations . In Vos , J. B. and Rizzi , A. (Eds.), Proceedings of the 9th GAMM Conference , vol. 35 , 201 .
   Google Scholar
• Mavriplis , D. J. ( 1997 ) Unstructured Grid Techniques . Annual Review of Fluid Mechanics , 29 , 473 – 514 .
   Web of Science ®Google Scholar
• Petzhold , L. ( 1983 ) A Description of DASSL: A Differential/Algebraic System Solver . In Stepleman , R. S. (Ed.) Scientific Computing , pp. 65 – 68 .
   Google Scholar
• Pletcher , R. H. and Chen , K. H. ( 1993 ) On Solving the Compressible Navier-Stokes Equations for Unsteady Flows at Very Low Mach Numbers . AIAA Paper 93-3368-CP .
   Google Scholar
• Riedel , U. , Maas , U. and Warnatz , J. ( l993a ) Detailed Numerical Modeling of Chemical and Thermal Nonequilibrium in Hypersonic Flows . Impact of Computing in Science and Engineering 5 , 20 – 52 .
   Google Scholar
• Riedel , U. , Maas , U. and Warnatz , J. ( 1993b ) Simulation of Nonequilibrium Hypersonic Flows . Computers & Fluids , 22 , 285 – 294 .
   Google Scholar
• Riedel , U. Publication in Preparation .
   Google Scholar
• Ruf , B. , Behrendt , F. , Deutschmann , O. and Warnatz , J. ( 1996 ) Simulation of Reactive Flow in Filament-Assisted Diamond Growth Including Hydrogen Surface Chemistry . Journal of Applied Physics , 79 , 7256 – 7263 .
   Google Scholar
• Saad , Y. ( 1990 ) SPARSKIT: A Basic Tool Kit Sparse Matrix Computations. Research Institute for Advanced Computer Science , NASA Ames Research Center , Moffet Field , CA , Technical Report 90 – 20 .
   Google Scholar
• Smooke , M. D. , Mitchell , R. E. and Keyes , D. E. ( 1989 ) Numerical Simulation of Two-Dimensional Axisymmetric Laminar Diffusion Flames . COMBUSTION SCIENCE AND TECHNOLOGY , 67 , 85 – 122 .
   Web of Science ®Google Scholar
• Thomadakis , M. and Leschziner , M. ( 1996 ) A Pressure-Correction Method for the Solution of Incompressible Viscous Flows On Unstructured Grids . International Journal for Numerical Methods in Fluids , 22 , 581 – 601 .
   Web of Science ®Google Scholar
• Turkel , E. ( 1987 ) Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations . Journal of Computational Physics , 72 , 277 – 298 .
   Web of Science ®Google Scholar
• Warnatz , J. ( 1992 ) Resolution of Gas Phase and Surface Combustion Chemistry into Elementary Reactions . Twenty-Fourth Symposium (International) on Combustion , The Combustion Institute , Pittsburgh , PA , pp. 553 – 579 .
   Google Scholar
• Warnatz , J. , Maas , U. and Dibble , R. W. ( 1996 Combustion , Springer Verlag , New York, Heidelberg .
   Google Scholar
• Williams , M. ( 1993 ) The Solution of the Two-Dimensional Incompressible Flow Equations on Unstructured Triangular Meshes . Numerical Heat Transfer , 23 , 309 – 325 .
   Web of Science ®Google Scholar