Geodesic
Discretization of Boltzmann equation with finite volume method and explicit-implicit schemes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 942-960

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The features of discretization of the Boltzmann equation using the finite volume method are considered. Finite-difference schemes for calculation of fluxes and finite-difference schemes for discretization in time are discussed. A TVD-type scheme is used for flux discretization, and an explicit-implicit scheme is applied to time discretization. The results of numerical simulation of rarefied gas flow in a shock tube for various Knudsen numbers are presented. For small Knudsen numbers, the solution of the Boltzmann equation is compared with the solution obtained from the Euler equation.
Keywords: finite volume method, Boltzmann equation, rarefied gas, shock tube. 
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     title = {Discretization of {Boltzmann} equation with finite volume method and explicit-implicit schemes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a55/}
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K. N. Volkov; V. N. Emelyanov; A. V. Pustovalov. Discretization of Boltzmann equation with finite volume method and explicit-implicit schemes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 942-960. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a55/