Geodesic
Efficient method for computing rarefied gas flow in a long finite plane channel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 288-303 Cet article a éte moissonné depuis la source Math-Net.Ru

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The linearized kinetic S-model is used to study the nonisothermal steady rarefied gas flow driven by differences in pressure and temperature in a plane channel between long finite parallel plates joining two tanks of infinite volume. An efficient composite (asymptotic) method is developed: a one-dimensional asymptotic solution corresponding to an infinitely long channel is constructed in the middle part of the computational domain, while a solution of the two-dimensional kinetic equation matched with the middle-part asymptotic solution is constructed near the ends of the channel. The latter solution is found numerically by a high-order accurate conservative method. The basic quantity to be computed is the gas flow rate through the channel. Characteristic flow features are also investigated. The resulting solutions are compared with previously known results. 
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V. A. Titarev; E. M. Shakhov. Efficient method for computing rarefied gas flow in a long finite plane channel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 2, pp. 288-303. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_2_a11/

[1] Sharipov F.M., Seleznev V.D., Dvizhenie razrezhennykh gazov v kanalakh i mikrokanalakh, UO RAN, Ekaterinburg, 2008

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

[3] Cercignani C., Neudachin I., “Rarefied gas flow through long slots”, Z. Angew. Math. und Phys., 30:6 (1979), 943–951 | DOI | MR | Zbl

[4] Akinshin V.D., Makarov A.I., Seleznev V.D., Sharipov F.M., “Techenie razrezhennogo gaza v ploskom kanale konechnoi dliny v shirokom diapazone chisel Knudsena”, Prikl. mekhan. i tekhn. fiz., 29:1 (1988), 105–111 | MR

[5] Akinshin V.D., Makarov A.I., Seleznev V.D., Sharipov F.M., “Dvizhenie razrezhennogo gaza v ploskom korotkom kanale vo vsem diapazone chisel Knudsena”, Prikl. mekhan. i tekhn. fiz., 30:5 (1989), 48–53

[6] Shakhov E.M., “Dvumernaya nelineinaya zadacha o dvizhenii razrezhennogo gaza mezhdu dvumya parallelnymi ploskostyami”, Zh. vychisl. matem. i matem. fiz., 35:1 (1995), 83–94 | MR | Zbl

[7] Larina I.N., Rykov V.A., “Raschet ploskikh techenii razrezhennogo gaza pri malykh chislakh Knudsena”, Zh. vychisl. matem. i matem. fiz., 36:12 (1996), 135–150 | MR | Zbl

[8] Larina I.N., Rykov V.A., Shaxov E.M., “Isparenie s poverkhnosti i istechenie para cherez ploskii kanal v vakuum”, Izv. RAN. Mekhan. zhidkosti i gaza, 1996, no. 1, 150–158 | Zbl

[9] Shakhov E.M., “Techenie razrezhennogo gaza cherez kanal i periodicheskuyu sistemu kanalov”, Izv. RAN. Mekhan. zhidkosti i gaza, 2000, no. 3, 166–175 | MR | Zbl

[10] Titarev V.A., “Conservative numerical methods for model kinetic equations”, Comput. and Fluids, 36:19 (2007), 1446–1459 | DOI | MR | Zbl

[11] Titarev B.A., “Chislennyi metod rascheta dvukhmernykh nestatsionarnykh techenii razrezhennogo gaza v oblastyakh proizvolnoi formy”, Zh. vychisl. matem. i matem. fiz., 49:7 (2009), 1255–1270 | MR | Zbl

[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] 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 | Zbl

[14] Titarev V.A., Shakhov E.M., “Neizotermicheskoe techenie gaza v dlinnom kanale na osnove kineticheskoi modeli”, Zh. vychisl. matem. i matem. fiz., 50:12 (2010), 2246–2260 | MR | Zbl

[15] Shakhov E.M., “Linearizirovannaya dvumernaya zadacha o techenii razrezhennogo gaza v dlinnom kanale”, Zh. vychisl. matem. i matem. fiz., 39:7 (1999), 1236–1245 | MR | Zbl

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

[17] 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

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

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

[20] Gropp W., Lusk E., Skjellum A., Using MPL Portable parallel programming with the message-passing interface, sec. ed., The MIT Press, 1999

[21] 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