Geodesic
Nonlinear nonequilibrium kinetic model of the Boltzmann equation for monatomic gases
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2084-2095 Cet article a éte moissonné depuis la source Math-Net.Ru

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A model kinetic equation approximating the Boltzmann equation in a wide range of nonequilibrium gas states was constructed to describe rarefied gas flows. The kinetic model was based on a distribution function depending on the absolute velocity of the gas particles. Highly efficient in numerical computations, the model kinetic equation was used to compute a shock wave structure. The numerical results were compared with experimental data for argon. 
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I. N. Larina; V. A. Rykov. Nonlinear nonequilibrium kinetic model of the Boltzmann equation for monatomic gases. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 2084-2095. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a11/

[1] Shakhov E. M., “Ob obobschenii relaksatsionnogo kineticheskogo uravneniya Kruka”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1968, no. 1, 156–161

[2] Larina I. N., Rykov V. A., “Modeli linearizovannogo integrala stolknovenii Boltsmana”, Zh. vychisl. matem. i matem. fiz., 47:6 (2007), 1029–1044 | MR

[3] Larina I. N., Rykov V. A., “Kineticheskaya model uravneniya Boltsmana, soderzhaschaya predelnye rezhimy techeniya gaza pri malykh chislakh Knudsena”, Zh. vychisl. matem. i matem. fiz., 47:7 (2008), 1294–1308 | MR

[4] Larina I. N., Rykov V. A., “Kineticheskaya model uravneniya Boltsmana dlya stepennogo potentsiala vzaimodeistviya mezhdu molekulami”, Zh. vychisl. matem. i matem. fiz., 50:3 (2010), 544–556 | MR | Zbl

[5] Cherchinyani K., Matematicheskie metody v kineticheskoi teorii gazov, Mir, M., 1973 | MR

[6] Vulikh B. Z., Vvedenie v funktsionalnyi analiz, Nauka, M., 1967 | MR | Zbl

[7] Larina I. N., Rykov V. A., “Chislennoe reshenie uravneniya Boltsmana metodom simmetrichnogo rasschepleniya”, Zh. vychisl. matem. i matem. fiz., 43:4 (2003), 601–613 | MR | Zbl

[8] Larina I. N., Rykov V. A., “Kineticheskaya model uravneniya Boltsmana dlya dvukhatomnogo gaza s vraschatelnymi stepenyami svobody”, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2233–2245 | MR | Zbl

[9] Ohwada T., “Structure of normal shock waves: Direct numerical analysis of the Boltzmann equation for hard-sphere molecules”, Phis. Fluids A5 (1), 5:3 (1993), 217–233 | DOI | MR

[10] Aristov V. V., Direct methods for solving the Boltzmann equation and study of nonequilibrium flows, Kluwer Acad. Publ., Dordrecht, 2001 | MR | Zbl

[11] Alsmeyer H., “Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam”, J. Fluid Mech., 74:3 (1976), 497–513 | DOI