Geodesic
Three-dimensional generalization for W-modification of a Godunov method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1659-1672 
E. I. Vasilev; A. S. Demin. Three-dimensional generalization for W-modification of a Godunov method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1659-1672. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a10/
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     title = {Three-dimensional generalization for {W-modification} of {a~Godunov} method},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A high-accuracy modification of Godunov's method for three-dimensional unsteady ideal gas flows is proposed. For the linear advection equation, a fully three-dimensional second-order accurate monotone scheme is designed with corrections computed on a variable stencil whose orientation depends on the signs of the equation coefficients. For the linear scalar advection equation, the scheme is proved to possess the positive approximation property. The method is tested by computing the flow in a three-dimensional Ludwieg tube with a square cross section.

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

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

[3] van Leer B., “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method”, J. Comput. Phys., 32 (1979), 101–136 | DOI

[4] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[5] Kopchenov V. I., Kraiko A. N., “Monotonnaya raznostnaya skhema vtorogo poryadka dlya giperbolicheskikh sistem s dvumya nezavisimymi peremennymi”, Zh. vychisl. matem. i matem. fiz., 23:2 (1983), 848–859 | MR | Zbl

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

[7] Rodionov A. V., “Povyshenie poryadka approksimatsii skhemy S. K. Godunova”, Zh. vychisl. matem. i matem. fiz., 27:12 (1987), 1853–1860 | MR | Zbl

[8] Colleta P., “Multidimensional upwind methods for hyperbolic conservation laws”, J. Comput. Phys., 87 (1990), 171–200 | DOI | MR

[9] Vasilev E. I., “$W$-modifikatsiya metoda C. K. Godunova i ee primenenie dlya dvumernykh nestatsionarnykh techenii zapylennogo gaza”, Zh. vychisl. matem. i matem. fiz., 36:1 (1996), 122–135 | MR

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

[11] Godunov S. K., Zabrodin A. B., Ivanov M. Ya. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl