A Semi-implicit Numerical Scheme for Reacting Flow: I. Stiff Chemistry

Journal of Computational Physics

Volumn 143, Issue 2, 1998, Pages 381-402

  Najm, Habib N ^a   Wyckoff, Peter S ^a   Knio, Omar M ^b  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b Johns Hopkins University   (United States)

Author keywords

Chemistry; Flow; Implicit; Projection; Reacting; Stiff

Indexed keywords

COMBUSTION; INTEGRAL EQUATIONS; POISSON EQUATION; VORTEX FLOW;

FLOW; IMPLICIT; PROJECTION; PROJECTION SCHEMES; REACTING; REACTING FLOWS; SECOND ORDERS; SEMI-IMPLICIT; STIFF; TWO-DIMENSIONS;

INTEGRATION;

EID: 0000752883     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1997.5856     Document Type: Article

References (62)

1. Aiken R. Stiff Computation. 1985.
2. Hairer E., Wanner G. Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems. 1996.
3. Curtiss C. F., Hirschfelder J. O. Integration of stiff equations. Proc. Nat. Acad. Sci. 38:1952;235.
4. Gear C. W. Numerical Initial Value Problems in Ordinary Differential Equations. 1971.
5. A. C. Hindmarsh, Lawrence Livermore National Laboratory, Livermore, CA, 1974.
6. A. C. Hindmarsh, Lawrence Livermore National Laboratory, Livermore, CA, 1977.
7. Hindmarsh A. C. LSODE and LSODI, two new initial value ordinary equation solvers. ACM-SIGNUM. 15:1980;10.
8. Hindmarsh A. C. Scientific Computing. 1983;55.
9. Brown P. N., Byrne G. D., Hindmarsh A. C. VODE: A variable coefficient ODE solver. SIAM J. Sci. Stat. Comput. 10:1989;1038.
10. H. H. Robertson, Numerical Analysis, An Introduction, J. Walsh, Academic Press, 1966, 178.
11. Saylor R. D., Ford G. D. On the comparison of numerical methods for the integration of kinetic equations in atmospheric chemistry and transport models. Atmos. Environ. 29:1995;2585.
12. Verwer J. G., van Loon M. An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics. J. Comput. Phys. 113:1994;347.
13. Radhakrishnan K. New integration techniques for chemical kinetic rate equations. I. Efficiency comparison. Combust. Sci. Technol. 46:1986;59.
14. D'Angelo Y., Larrouturou B. Comparison and analysis of some numerical schemes for stiff complex chemistry problem. RAIRO. Math. Model. and Numer. Anal. 29:1995;259.
15. Verwer J. G. Gauss-Seidel iteration for stiff ODES from chemical kinetics. SIAM J. Sci. Comput. 15:1994;1234.
16. Verwer J. G., Blom J. G., Spee E. J. A comparison of stiff ODE solvers for atmospheric chemistry problems. Atmos. Environ. 30:1996;49.
17. Aro C. J. CHEMSODE: A stiff ODE solver for the equations of chemical kinetics. Comput. Phys. Commun. 97:1996;304.
18. Baeza, Baeza J. J., Plá, Pérez F., Ramos, Ramis G. Stiffness-adaptive taylor method for the integration of non-stiff and stiff kinetic models. J. Comput. Chem. 13:1992;810.
19. Sun P., Chock D. P., Winkler S. L. An implicit-explicit hybrid solver for a system of stiff kinetic equations. J. Comput. Phys. 115:1994;515.
20. Chock D. P., Winkler S. L., Sun P. Comparison of stiff chemistry solvers for air quality modeling. Environ. Sci. Technol. 28:1994;1882.
21. Dabdub D., Seinfeld J. H. Extrapolation techniques used in the solution of stiff ODEs associated with chemical kinetics of air quality models. Atmos. Environ. 29:1995;403.
22. Elliot S., Turco R. P., Jacobson M. Z. Tests on combined projection/forward differencing integration for stiff photochemical family systems at long time step. Comput. Chem. 17:1993;91.
23. Hesstvedt E., Hov O., Isaksen I. S. A. Quasi-steady-state approximations in air pollution modeling: Comparison of two numerical schemes for oxidant prediction. Int. J. Chem. Kinetics. 10:1978;971.
24. Young T. R., Boris J. P. A numerical technique for solving stiff ordinary differential equations associated with the chemical kinetics of reactive flow problems. J. Phys. Chem. 81:1977;2424.
25. Gong W., Cho H.-R. A numerical scheme for the integration of the gas-phase chemical rate equations in three-dimensional atmospheric models. Atmos. Environ. 27A:1993;2591.
26. Radhakrishnan K. Integrating combustion kinetic rate equations by selective use of stiff and nonstiff methods. AIAA J. 25:1987;1449.
27. Goyal G., Paul P. J., Mukunda H. S., Deshpande S. M. Time dependent operator-split and unsplit schemes for one dimensional premixed flames. Combust. Sci. Tech. 60:1988;167.
28. Zhong X. Additive semi-implicit Runge-Kutta methods for computing high-speed nonequilibrium reactive flows. J. Comput. Phys. 128:1996;19.
29. U. Mass, S. B. Pope, Twenty-Fourth Symposium (International) on Combustion, The Combustion Institute, 1992, 103.
30. S. Mahalingam, B. J. Cantwell, J. H. Ferziger, Thermosciences Division, Dept. of Mechanical Engineering, Stanford University, Stanford, CA, 1989.
31. E. S. Oran, Computational Fluid Dynamics and Reacting Gas Flows, A. M. M. LuskinB. Engquist, Springer-Verlag, New York, 1988, 291.
32. 22. AIAA J. 32:1994;84.
33. Najm H. N., Wyckoff P. S. Premixed flame response to unsteady strain-rate and curvature. Combust. Flame. 110:1997;92.
34. H. N. Najm, Transport Phenomena in Combustion, S. Chan, 2, Taylor & Francis, Washington, DC, 1996, 921.
35. Majda A., Sethian J. The derivation and numerical solution of the equations for zero mach number combustion. Combust. Sci. and Technol. 42:1985;185.
36. A. F. Ghoniem, O. M. Knio, Twenty-First Symposium (International) on Combustion, The Combustion Institute, 1986, 1313.
37. O. M. Knio, A. S. Worlikar, H. N. Najm, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, 1996, 203.
38. Schlichting H. Boundary-Layer Theory. 1979.
39. Williams F. A. Combustion Theory. 1985.
40. R. J. Kee, F. M. Rupley, J. A. Miller, Sandia National Labs. Livermore, CA, 1993.
41. Chorin A. J. A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2:1967;12.
42. Kim J., Moin P. Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59:1985;308.
43. McMurtry P. A., Jou W.-H., Riley J. J., Metcalfe R. W. Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24:1986;962.
44. Mahalingam S., Cantwell B. J., Ferziger J. H. Full numerical simulations of coflowing, axisymmetric jet diffusion flames. Physics of Fluids A. 2:1990;720.
45. Anderson D. A., Tannehill J. C., Pletcher R. H. Computational Fluid Mechanics and Heat Transfer. 1984.
46. C. Rutland, J. H. Ferziger, B. J. Cantwell, Mech. Eng. Stanford Univ. Stanford, CA, 1989.
47. Rutland C. J., Ferziger J. H. Simulations of flame-vortex interactions. Combust. Flame. 84:1991;343.
48. M. Frenklach, H. Wang, M. Goldenberg, G. P. Smith, D. M. Golden, C. T. Bowman, R. K. Hanson, W. C. Gardiner, V. Lissianski, Gas Research Institute, 1995.
49. R. J. Kee, J. F. Grcar, M. D. Smooke, J. A. Miller, Sandia National Labs. Livermore, CA, 1993.
50. Ashurst W. T., McMurtry P. A. Flame generation of vorticity: Vortex dipoles from monopoles. Combust. Sci. and Technol. 66:1989;17.
51. Poinsot T., Veynante D., Candel S. Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228:1991;561.
52. T. Mantel, Center for Turbulence Research, Stanford University/NASA Ames Research Center, 1994.
53. Hilka M., Veynante D., Baum M., Poinsot T. J. Tenth Symp. on Turbulent Shear Flows. 2:1995;19.
54. J. Jarosinski, J. H. Lee, R. Knystautas, Twenty-Second Symposium (International) on Combustion, The Combustion Institute, 1988, 505.
55. Roberts W. L., Driscoll J. F., Drake M. C., Goss L. P. Images of the quenching of a flame by a vortex-to quantify regimes of turbulent combustion. Combust. Flame. 94:1993;58.
56. J.-M. Samaniego, Center for Turbulence Research, Stanford University/NASA Ames Research Center, 1993.
57. Mueller C. J., Driscoll J. F., Sutkus D. J., Roberts W. L., Drake M. C., Smooke M. D. Effect of unsteady stretch rate on OH chemistry during a flame-vortex interaction: To assess flamelet models. Combust. Flame. 100:1995;323.
58. Q.-V. Nguyen, P. H. Paul, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, 1996, 357.
59. Mueller C. J., Driscoll J. F., Reuss D. L., Drake M. C., Rosalik M. E. Vorticity generation and attenuation as vortices convect through a premixed flame. Combust. Flame. 112:1998;342.
60. N. Peters, Turbulent Reactive Flows, R. BorghiS. Murthy, Springer-Verlag, New York, 1989, 242.
61. Darabiha N., Candel S. M., Marble F. E. The effect of strain rate on a premixed laminar flame. Combust. Flame. 64:1986;203.
62. I. Gran, T. Echekki, J. H. Chen, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, 1996, 323.