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Upwind computation of steady planar flames with complex chemistry. (English) Zbl 0717.65109
The study reported in this paper aims at designing an upwind scheme of finite element Petrov-Galerkin type for the simulation of planary steady premixed flames with complex chemistry. The resulting scheme is shown to preserve the positivity of the mass fractions of all species and to give non-oscillatory results for any values of the local cell Reynolds number and of the time step while remaining second order accurate.
Reviewer: P.K.Mahanti

MSC:
65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80A30 Chemical kinetics in thermodynamics and heat transfer
35Q80 Applications of PDE in areas other than physics (MSC2000)
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References:
[1] A. K. Aziz ed, The mathematical foundations of the finite-element method withapplications to partial differential equations, Academic Press, NewYork (1972) Zbl0259.00014 MR347104 · Zbl 0259.00014
[2] P. G. ClARLET, The finite-element method for elliptic problems, Studies in Math and Appl, North-Holland, New York (1978) Zbl0383.65058 MR520174 · Zbl 0383.65058
[3] P. CLAVIN, Dynamic behavior of premixed flame fronts in laminar and turbulent flows, Prog Energ Comb Sci, 11, pp 1-59 (1985)
[4] J. DONEA, Recent advances in computational methods for steady and transient transport problems, Nuclear Eng Design, 80, pp 141-162 (1984)
[5] M. GHILANI, Simulation numérique de flammes planes stationnaires avec chimiecomplexe, Thesis, Université Paris-Sud (1987)
[6] D. F. GRIFFITHS & J. LORENZ, An analysis of the Petrov-Galerkin finite-element method, Comp Meth Appl Mech Eng, 14, pp 39-64 (1978) Zbl0384.76065 MR502036 · Zbl 0384.76065 · doi:10.1016/0045-7825(78)90012-9
[7] T. J. R. HUGHES, A simple scheme for developing upwindfïnite éléments, Int. J. Num. Meth. Eng., 12, pp. 1359-1365 (1978). Zbl0393.65044 · Zbl 0393.65044 · doi:10.1002/nme.1620120904
[8] B. LARROUTUROU, The equations of one-dimensional unsteady flame propagation : existence and uniquenes, SI AM J. Math. Anal., 19 (1), pp. 32-59 (1988). Zbl0662.35090 MR924543 · Zbl 0662.35090 · doi:10.1137/0519003
[9] B. LARROUTUROU, Introduction to combustion modelling, Springer Series in Computational Physics, to appear. · Zbl 0744.76112
[10] N. PETERS & J. WARNATZ eds, Numerical methods in laminar flame propagation, Notes in Numerical Fluid Mechanics, 6, Vieweg, Braunschweig (1982). Zbl0536.00017 MR736841 · Zbl 0536.00017
[11] R. D. RJCHTMYER & K. W. MORTON, Difference methods for initial value problems, Wiley, New York (1967). Zbl0155.47502 · Zbl 0155.47502
[12] M. SERMANGE, Mathematical and numerical aspects of one-dimensional laminar flame simulation, Appl. Math. Opt., 14 (2), pp. 131-154 (1986). Zbl0654.65085 MR863336 · Zbl 0654.65085 · doi:10.1007/BF01442232
[13] M. D. SMOOKE, Solution of burner stabilized premixed laminar flames by boundary values methods, J. Comp. Phys., 48, pp. 72-105 (1982). Zbl0492.65065 · Zbl 0492.65065 · doi:10.1016/0021-9991(82)90036-5
[14] M. D. SMOOKE, J. A. MILLER & R. J. KEE, Determination of adiabatic flames speeds by boundary value methods, Comb. Sci. Tech., 34, pp. 79-90 (1983).
[15] R. F. WARMING & F. HYETT, The modified equation approach to the stabilityand accuracy analysis of finite-difference methods, J. Comp. Phys., 14 (2), p.159 (1974). Zbl0291.65023 MR339526 · Zbl 0291.65023 · doi:10.1016/0021-9991(74)90011-4
[16] F. A. WILLIAMS, Combustion theory, second édition, Benjamin Cummings, Menlo Park (1985).
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