Geodesic
Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 10, pp. 1811-1826 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The method based on the numerical solution of a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The basic idea behind the method is the use of a second-order accurate TVD scheme on hybrid unstructured meshes in physical space and a fast implicit time discretization method without iterations at the upper level. The performance of the method is illustrated by computing test examples of three-dimensional rarefied gas flows in variously shaped channels in a wide range of Knudsen numbers. 
@article{ZVMMF_2010_50_10_a7,
     author = {V. A. Titarev},
     title = {Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1811--1826},
     year = {2010},
     volume = {50},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_10_a7/}
}
TY  - JOUR
AU  - V. A. Titarev
TI  - Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1811
EP  - 1826
VL  - 50
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_10_a7/
LA  - ru
ID  - ZVMMF_2010_50_10_a7
ER  - 
%0 Journal Article
%A V. A. Titarev
%T Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1811-1826
%V 50
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_10_a7/
%G ru
%F ZVMMF_2010_50_10_a7
V. A. Titarev. Implicit numerical method for computing three-dimensional rarefied gas flows on unstructured meshes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 10, pp. 1811-1826. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_10_a7/

[1] Li Z.-H., Zhang H.-X., “Study on gas kinetic unified algorithm for flows from rarefied transition to continuum”, J. Comput. Phys., 193:2 (2004), 708–738 | DOI | Zbl

[2] Kolobov V. I., Arslanbekov R. R., Aristov V. V. et al., “Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement”, J. Comput. Phys., 223 (2007), 589–608 | DOI | Zbl

[3] Shakhov E. M., “Ob obobschenii relaksatsionnogo kineticheskogo uravneniya Kruka”, Izv. AN SSSR. MZhG, 1968, no. 5, 142–145

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

[5] 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

[6] 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

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

[8] 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

[9] Shakhov E. M., “O priblizhennykh kineticheskikh uravneniyakh v teorii razrezhennykh gazov”, Izv. AN SSSR. MZhG, 1968, no. 1, 158–161

[10] 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

[11] Dumbser M., Käser M., “Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems”, J. Comput. Phys., 221:2 (2007), 693–723 | DOI | MR | Zbl

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

[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] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001 | MR

[16] Venkatakrishnan V., On the accuracy of limiters and convergence to steady-state solutions, AIAA paper 93-0880

[17] Aristov V. V., Cheremisin F. G., “Konservativnyi metod rasschepleniya dlya resheniya uravneniya Boltsmana”, Zh. vychisl. matem. i matem. fiz., 20:1 (1980), 191–207 | MR | Zbl

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

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

[20] Titarev V. 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

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

[22] 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

[23] Bishaev A. M., Rykov V. A., “Perekondensatsiya odnoatomnogo gaza pri malykh chislakh Knudsena”, Zh. vychisl. matem. i matem. fiz., 18:3 (1978), 710–717