Geodesic
Numerical analysis of the spiral Couette flow of a rarefied gas between coaxial cylinders
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 527-535 
V. A. Titarev; E. M. Shakhov. Numerical analysis of the spiral Couette flow of a rarefied gas between coaxial cylinders. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 3, pp. 527-535. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_3_a15/
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     author = {V. A. Titarev and E. M. Shakhov},
     title = {Numerical analysis of the spiral {Couette} flow of a rarefied gas between coaxial cylinders},
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Voir la notice de l'article provenant de la source Math-Net.Ru

An implicit quasi-monotone second-order accurate method is proposed for analyzing the spiral Couette flow of a rarefied gas between coaxial cylinders. The basic advantages of the method over the conventional method of stationry iterations are that the former is conservative with respect to the collision integral, has a simple software implementation for any types of boundary conditions, and applies to a wide range of Knudsen numbers.

[1] Soga T., Oguchi H., “A nonlinear analysis of cylindrical Couette flow”, Rarefied Gas Dynamics, Proc. 9th Internat. Symp., DFVLR Press. Porz-Wahn, Germany, 1974, Paper No A.17

[2] Sharipov F. M., Kremer G. M., “Non-isothermal Couette flow of a rarefied gas between two rotating cylindres”, European J. Mech. – B/Fluids, 18:1 (1999), 121–130 | DOI | Zbl

[3] Aoki K., Yoshida H., Nakanishi T., “Inverted velocity profile in the cylindrical Couette flow of a rarefied gas”, Phys. Rev. E, 68 (2003), 016302 | MR

[4] Shakhov E. M., “Ustanovivsheesya techenie razrezhennogo gaza ot sfericheskogo istochnika ili stoka”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1971, no. 2, 58–66 | Zbl

[5] Bishaev A. M., Rykov B. A., “Reshenie statsionarnykh zadach kineticheskoi teorii gazov pri umerennykh i malykh chislakh Knudsena metodom iteratsii”, Zh. vychisl. matem. i matem. fiz., 15:1 (1975), 172–182 | Zbl

[6] Godunov S. K., “Raznostnyi metod chislennogo rascheta razryvnykh reshenii uravnenii gidrodinamiki”, Matem. sb., 47(89):3 (1959), 271–306 | MR | Zbl

[7] Shakhov E. M., “Ob obobschenii relaksatsionnogo kineticheskogo uravneniya Kruka”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 3:5 (1968), 142–145

[8] Shakhov E. M., Metod issledovaniya dvizhenii razrezhennogo gaza, Nauka, M., 1974

[9] Chu C. K., “Kinetic-theoretic description of the formation of a shock wave”, Phys. Fluids, 8:1 (1965), 12–22 | DOI

[10] Bishaev A. M., Rykov V. A., “O prodolnom potoke tepla v techenii Kuetta”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1980, no. 3, 162–166 | Zbl

[11] Larina I. N., Rykov V. A., “Chislennyi metod rascheta osesimmetrichnykh techenii razrezhennogo gaza”, Zh. vychisl. matem. i matem. fiz., 38:8 (1998), 1391–1403 | MR | Zbl

[12] Ivanov M. Ya., Nigmatullin R. Z., “Neyavnaya skhema S. G. Godunova povyshennoi tochnosti dlya chislennogo integrirovaniya uravnenii Eilera”, Zh. vychisl. matem. i matem. fiz., 27:11 (1987), 1725–1735 | MR | Zbl

[13] Yang J. Y., Huang J. C., “Rarefied flow computations using nonlinear model Boltzmann equations”, J. Comput. Phys., 120:2 (1995), 323–339 | DOI | Zbl

[14] Kolgan V. P., “Primenenie printsipa minimalnykh znachenii proizvodnoi k postroeniyu konechno-raznostnykh skhem dlya rascheta razryvnykh techenii gazovoi dinamiki”, Uch. zap. TsAGI, 3:6 (1972), 68–77

[15] Kolgan V. P., “Konechno-raznostnaya skhema dlya rascheta dvukhmernykh razryvnykh techenii nestatsionarnoi gazovoi dinamiki”, Uch. zap. TsAGI, 6:1 (1975), 9–14

[16] Gradoboev M. I., Rykov V. A., “Konservativnyi metod chislennogo resheniya kineticheskogo uravneniya pri malykh chislakh Knudsena”, Zh. vychisl. matem. i matem. fiz., 34:2 (1994), 246–266 | MR | Zbl

[17] Mieussens L., “Discrete-velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries”, J. Comput. Phys., 162:2 (2000), 429–466 | DOI | MR | Zbl

[18] Gusarov A. V., Smurov I., “Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer”, Phys. Fluids, 14:12 (2002), 4242–4255 | DOI | MR

[19] Titarev B. A., Shakhov E. M., “Chislennoe issledovanie silnogo nestatsionarnogo ispareniya s poverkhnosti sfery”, Zh. vychisl. matem. i matem. fiz., 44:7 (2004), 1314–1328 | MR | Zbl