Geodesic
Method for solving the Boltzmann kinetic equation for polyatomic gases
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 270-287

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A method is proposed for computing the collision operator of a generalized Boltzmann kinetic equation with allowance for energy transfer from translational to vibrational or rotational degrees of freedom. The collision operator is computed using a projection method on a uniform velocity grid. The operator satisfies the mass, momentum, and energy conservation laws and vanishes for an equilibrium velocity distribution function. Approximate models are suggested that provide savings on the computation of rotational-translational relaxation. Numerical examples are presented. 
@article{ZVMMF_2012_52_2_a10,
     author = {F. G. Tcheremissine},
     title = {Method for solving the {Boltzmann} kinetic equation for polyatomic gases},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {270--287},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a10/}
}
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F. G. Tcheremissine. Method for solving the Boltzmann kinetic equation for polyatomic gases. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 270-287. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a10/