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A gas-kinetic scheme for reactive flows. (English) Zbl 0977.76072
Summary: The gas-kinetic BGK scheme for compressible flow equations is extended to chemical reactive flow. The mass fraction of unburnt gas is implemented into the gas kinetic formulation by assigning a new internal degree of freedom to the particle distribution function. This new variable can be also used to describe the fluid trajectory for nonreactive flows. The gas-kinetic BGK model successfully solves the Navier-Stokes chemical reactive flow equations. Numerical examples validate the accuracy and robustness of the current approach.

76M28 Particle methods and lattice-gas methods
76V05 Reaction effects in flows
80A32 Chemically reacting flows
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[1] Bhatnagar, P.L.; Gross, E.P.; Krook, M., A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems, Phys. rev, 94, 511-525, (1954) · Zbl 0055.23609
[2] Bourlioux A. Numerical study of unsteady detonations. PhD Thesis, Princeton University, 1991
[3] Colella, P.; Majda, A.; Roytburd, V., Theoretical and numerical structure for reacting shock wave, SIAM J. sci. stat. comput, 7, 4, 1059-1080, (1986) · Zbl 0633.76060
[4] Engquist B, Sjogreen B. Robust difference approximations of stiff inviscid detonation waves. Research Report, Computational and Applied Mathematics, UCLA, 1991 · Zbl 0789.35104
[5] Erpenbeck, J.J., Stability of idealized one-reaction detonation, Phys. fluids, 7, 684-696, (1964) · Zbl 0123.42901
[6] Fickett, W.; Davis, W.C., Detonation, (1979), University of California Press Berkeley, CA
[7] Fickett, W.; Wood, W.W., Flow calculations for pulsating one-dimensional detonations, Phys. fluids, 9, 903-916, (1966)
[8] Hwang P, Fedkiw RP, Merriman B, Karagozian AR, Osher SJ. Numerical resolution of pulsating detonation. UCLA CAM Report 99-12, 1999
[9] Jeltsch R, Klingenstein P. Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting. Research Report No. 97-16, ETH, Switzerland, 1997 · Zbl 0970.65100
[10] Kim, C.; Jameson, A., A robust and accurate LED-BGK solver on unstructured adaptive meshes, J. comput. phys, 143, 598-627, (1998) · Zbl 0936.76042
[11] Kotelnikov, A.D.; Montgomery, D.C., A kinetic method for computing inhomogeneous fluid behavior, J. comput. phys, 134, 364-388, (1997) · Zbl 0887.76053
[12] Lindstrom D. Numerical computation of viscous detonation waves in two space dimensions. Research Report, Department of Scientific Computing, Uppsala University, Uppsala, Sweden, 1996
[13] Mandal, J.C.; Deshpande, S.M., Kinetic flux vector splitting for Euler equations, Computers fluids, 23, 447-478, (1994) · Zbl 0811.76047
[14] Mulder, M.; Osher, S.; Sethian, J.A., Computing interface motion in compressible gas dynamics, J. of comput. phys, 100, 209-228, (1992) · Zbl 0758.76044
[15] Pullin, D.I., Direct simulation methods for compressible inviscid ideal-gas flow, J. of comput. phys, 34, 231, (1980) · Zbl 0419.76049
[16] Quirk J. Godunov-type schemes applied to detonation flows. ICASE Report 93-15, 1993
[17] Woodward, P.; Colella, P., Numerical simulations of two-dimensional fluid flow with strong shocks, J. comput. phys, 54, 115, (1984) · Zbl 0573.76057
[18] Xu K. Gas-kinetic schemes for unsteady compressible flow simulations, 29th CFD Lecture Series, von Karman Institute for Fluid Dynamics, 1998
[19] Xu, K.; Kim, C.; Martinelli, L.; Jameson, A., BGK-based schemes for the simulation of compressible flow, Int. J. of comput. fluid dynamics, 7, 213-235, (1996) · Zbl 0896.76076
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