Geodesic
Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-Model
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2246-2260 Cet article a éte moissonné depuis la source Math-Net.Ru

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The nonisothermal steady rarefied gas flow driven by a given pressure gradient (Poiseuille flow) or a temperature gradient (thermal creep) in a long channel (pipe) of an arbitrary cross section is studied on the basis of the linearized kinetic S-model. The solution is constructed using a high-order accurate conservative method. The numerical computations are performed for a circular pipe and for a cross section in the form of a regular polygon inscribed in a circle. The basic characteristic of interest is the gas flow rate through the channel. The solutions are compared with previously known results. The flow rates computed for various cross sections are also compared with the corresponding results for a circular pipe. 
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V. A. Titarev; E. M. Shakhov. Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-Model. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2246-2260. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a13/

[1] Sharipov F., Seleznev V., “Data on internal rarefied gas flows”, J. Phys. Chem. Ref. Data, 27:3 (1998), 657–706 | DOI | MR

[2] Sharipov F. M., Seleznev V. D., Dvizhenie razrezhennykh gazov v kanalakh i mikrokanalakh, UrO RAN, Ekaterinburg, 2008, 230 pp.

[3] Bhathnagar P. L., Gross E. P., Krook M., “A model for collision processes in gases. I: Small amplitude processes in charged and neutral one-component systems”, Phys. Rev., 94:3 (1954), 511–525 | DOI

[4] Shakhov E. M., “Ob obobschenii relaksatsionnogo kineticheskogo uravneniya Kruka”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1968, no. 5, 142–145

[5] Loyalka S. K., “Kinetic theory of thermal transpiration and mechanocaloric effect, I”, J. Chem. Phys., 55:9 (1971), 4497–4503 | DOI

[6] Loyalka S. K., “Kinetic theory of thermal transpiration and mechanocaloric effect, II”, J. Chem. Phys., 63:9 (1975), 4054–4060 | DOI

[7] Loyalka S. K., Storvik T. S., Park H. S., “Poiseuille flow and thermal creep flow in long, rectangular channels in the molecular and transition flow regimes”, J. Vac. Sci. Technol. A, 5 (1976), 1188–1192

[8] Sharipov F. M., “Non-isothermal gas flow through long rectangular microchannels”, J. Micromech. Microeng., 1999, no. 9, 394–401 | DOI

[9] Graur I., Sharipov F., “Non-isothermal flow of rarefied gas through a long pipe with elliptic cross section”, Microfluidics and Nanofluidics, 6:2 (2009), 267–275 | DOI

[10] Titarev V. A., “Chislennyi metod rascheta dvukhmernykh nestatsionarnykh techenii razrezhennogo gaza v oblastyakh proizvolnoi formy”, Zh. vychisl. matem. i matem. fiz., 49:7 (2009), 1–16 | MR

[11] Titarev V. A., Shakhov E. M., “Konservativnyi metod vysokogo poryadka dlya rascheta techeniya Puazeilya razrezhennogo gaza v kanale proizvolnogo poperechnogo secheniya”, Zh. vychisl. matem. i matem. fiz., 50:3 (2010), 563–574 | MR

[12] Titarev V. A., “Implicit unstructured-mesh method for calculating Poiseuille flows of rarefied gas”, Communs Comput. Phys., 8:2 (2010), 427–444 | MR

[13] 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

[14] Tillyaeva N. I., “Obobschenie modifitsirovannoi skhemy S. K. Godunova na proizvolnye neregulyarnye setki”, Uch. zap. TsAGI, 17:2 (1986), 18–26

[15] van der Vegt J. J. W., van der Ven H., “Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid comporessible flows”, J. Comput. Phys., 141:1 (1998), 46–77 | DOI | MR | Zbl

[16] Titarev V. A., Shakhov E. M., “Chislennyi raschet poperechnogo obtekaniya kholodnoi plastiny giperzvukovym potokom razrezhennogo gaza”, Izv. RAN. Mekhan. zhidkosti i gaza, 2005, no. 5, 139–154 | Zbl

[17] Titarev V. A., “Conservative numerical methods for model kinetic equations”, Comput. and Fluids, 36:9 (2007), 1446–1459 | DOI | MR | Zbl

[18] Men'shov I. S., Nakamura Y., “An implicit advection upwind splitting scheme for hypersonic air flows in thermochemical nonequilibrium”, Collect. Techn. Papers of 6th Internat. Symp. on CFD (Lake Tahoe, Nevada, 1995), v. 2, 815

[19] Men'shov I. S., Nakamura Y., “On implicit Godunov's method with exactly linearized numerical flux”, Comput. and Fluids, 29:6 (2000), 595–616 | DOI

[20] Aristov V. V., Zabelok S. A., “Deterministicheskii metod resheniya uravneniya Boltsmana s parallelnymi vychisleniyami”, Zh. vychisl. matem. i matem. fiz., 42:3 (2002), 425–437 | MR | Zbl

[21] Lo S. S., Loyalka S. K., “An efficient computation of near-continuum rarefied gas flows”, J. Appl. Math. and Phys. (ZAMP), 33 (1982), 419–424 | DOI | Zbl