Geodesic
A modification of the CABARET scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics
Numerical methods and programming, Tome 18 (2017) no. 1, pp. 1-10.

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An algorithm for numerical simulation of one-dimensional detonation using a one-stage irreversible model of chemical kinetics is proposed. The discretization of the convective parts of governing equations is made in accordance with the balance-characteristic CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) approach. The approximation of source terms is performed implicitly without splitting into physical processes with a regulated order of approximation. It is shown that the numerically obtained Chapman-Jouget detonation parameters are in exact agreement with the analytical solution. It is also shown that, in the case of unstable detonation, the numerical results are dependent on the order of approximation chosen for the right-hand sides of the governing equations.
Keywords: one-velocity multicomponent medium, systems of hyperbolic equations, computational fluid dynamics (CFD), conservative methods, detonation, Arrhenius reaction.
Mots-clés : CABARET scheme 
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     author = {A. V. Danilin and A. V. Solov'ev and A. M. Zaitsev},
     title = {A modification of the {CABARET} scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics},
     journal = {Numerical methods and programming},
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     publisher = {mathdoc},
     volume = {18},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_1_a0/}
}
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A. V. Danilin; A. V. Solov'ev; A. M. Zaitsev. A modification of the CABARET scheme for numerical simulation of one-dimensional detonation flows using a one-stage irreversible model of chemical kinetics. Numerical methods and programming, Tome 18 (2017) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/VMP_2017_18_1_a0/