×

zbMATH — the first resource for mathematics

A semi-implicit numerical scheme for reacting flow. I: Stiff chemistry. (English) Zbl 0936.76064
The authors construct an additive semi-implicit projection scheme for simulation of unsteady combustion in two dimensions. The scheme relies on a zero-Mach number formulation of the compressible conservation equations with detailed chemistry. The governing equations are discretized in space using second-order differences, and integrated in time using a semi-implicit approach. Time integration of the evolution equations for species mass fraction, thermodynamic pressure, and density is performed using a semi-implicit, nonsplit scheme that combines a second-order predictor-corrector treatment of convection and diffusion terms, and a stiff integrator for the reaction source terms. Possible extensions of the present scheme to further improve efficiency are also discussed.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76V05 Reaction effects in flows
92E20 Classical flows, reactions, etc. in chemistry
80A25 Combustion
Software:
CHEMSODE; CHEMKIN; RODAS; VODE
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aiken, R., Stiff computation, (1985) · Zbl 0607.65041
[2] Hairer, E.; Wanner, G., Solving ordinary differential equations II, stiff and differential-algebraic problems, (1996) · Zbl 0859.65067
[3] Curtiss, C.F.; Hirschfelder, J.O., Integration of stiff equations, Proc. nat. acad. sci., 38, 235, (1952) · Zbl 0046.13602
[4] Gear, C.W., Numerical initial value problems in ordinary differential equations, (1971) · Zbl 0217.21701
[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, 10, (1980)
[8] Hindmarsh, A.C., Scientific computing, 55, (1983)
[9] Brown, P.N.; Byrne, G.D.; Hindmarsh, A.C., VODE: A variable coefficient ODE solver, SIAM J. sci. stat. comput., 10, 1038, (1989) · Zbl 0677.65075
[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, 2585, (1995)
[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, 347, (1994) · Zbl 0810.65068
[13] Radhakrishnan, K., New integration techniques for chemical kinetic rate equations. I. efficiency comparison, Combust. sci. technol., 46, 59, (1986)
[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, 259, (1995) · Zbl 0829.76062
[15] Verwer, J.G., Gauss-Seidel iteration for stiff ODES from chemical kinetics, SIAM J. sci. comput., 15, 1234, (1994) · Zbl 0804.65068
[16] Verwer, J.G.; Blom, J.G.; Spee, E.J., A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmos. environ., 30, 49, (1996)
[17] Aro, C.J., CHEMSODE: A stiff ODE solver for the equations of chemical kinetics, Comput. phys. commun., 97, 304, (1996) · Zbl 0926.65072
[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, 810, (1992)
[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, 515, (1994) · Zbl 0812.65061
[20] Chock, D.P.; Winkler, S.L.; Sun, P., Comparison of stiff chemistry solvers for air quality modeling, Environ. sci. technol., 28, 1882, (1994)
[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, 403, (1995)
[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, 91, (1993)
[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, 971, (1978)
[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, 2424, (1977)
[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, 2591, (1993)
[26] Radhakrishnan, K., Integrating combustion kinetic rate equations by selective use of stiff and nonstiff methods, Aiaa j., 25, 1449, (1987)
[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, 167, (1988)
[28] Zhong, X., Additive semi-implicit runge – kutta methods for computing high-speed nonequilibrium reactive flows, J. comput. phys., 128, 19, (1996) · Zbl 0861.76057
[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] Katta, V.R.; Goss, L.P.; Roquemore, W.M., Numerical investigations of transitional H_{2}2, Aiaa j., 32, 84, (1994) · Zbl 0825.76553
[33] Najm, H.N.; Wyckoff, P.S., Premixed flame response to unsteady strain-rate and curvature, Combust. flame, 110, 92, (1997)
[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, 185, (1985)
[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, 12, (1967) · Zbl 0149.44802
[42] Kim, J.; Moin, P., Application of a fractional-step method to incompressible navier – stokes equations, J. comput. phys., 59, 308, (1985) · Zbl 0582.76038
[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, 962, (1986)
[44] Mahalingam, S.; Cantwell, B.J.; Ferziger, J.H., Full numerical simulations of coflowing, axisymmetric jet diffusion flames, Physics of fluids A, 2, 720, (1990)
[45] Anderson, D.A.; Tannehill, J.C.; Pletcher, R.H., Computational fluid mechanics and heat transfer, (1984) · Zbl 0569.76001
[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, 343, (1991)
[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, 17, (1989)
[51] Poinsot, T.; Veynante, D.; Candel, S., Quenching processes and premixed turbulent combustion diagrams, J. fluid mech., 228, 561, (1991)
[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, 19, (1995)
[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, 58, (1993)
[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, 323, (1995)
[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, 342, (1998)
[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, 203, (1986)
[62] I. Gran, T. Echekki, J. H. Chen, Twenty-Sixth Symposium (International) on Combustion, The Combustion Institute, 1996, 323
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.