Geodesic
Third-order accurate finite-volume method on a triangular grid
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1918-1930 Cet article a éte moissonné depuis la source Math-Net.Ru

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A third-order accurate finite-volume method on triangular grids is proposed for the numerical solution of conservation law systems. The method is described in detail as applied to the advection equation. The accuracy of its numerical solutions obtained on grids of various degrees of detail is compared. The viscous flow over a plate and the unsteady flow around a cylinder are solved. For comparison purposes, the latter problem is also solved using third- and fifth-order accurate compact approximations. 
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     title = {Third-order accurate finite-volume method on a~triangular grid},
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D. A. Shirobokov. Third-order accurate finite-volume method on a triangular grid. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1918-1930. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a14/

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

[2] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Nauka, M., 1987 | MR

[3] Tolstykh A. I., Shipobokov D. A., “O paznostnykh skhemakh s kompaktnymi apppoksimatsiyami pyatogo popyadka dlya ppostpanstvennykh techenii vyazkogo gaza”, Zh. vychisl. matem. i matem. fiz., 36:4 (1996), 71–85 | MR | Zbl

[4] Tolstykh A. I., “Ob odnom metode chislennogo pesheniya upavneniya Nave–Stoksa szhimaemogo gaza”, Uch. zap. TsAGI, 3:6 (1972), 78–87

[5] Tolstykh A. I., “Ob odnom klasse netsentrirovannykh kompaktnykh raznostnykh skhem pyatogo poryadka osnovannykh na approksimatsiyakh Pade”, Dokl. AN SSSR, 319:1 (1991), 72–77 | MR | Zbl

[6] Marsden O., Bogey Ch., Bailly Ch., “High-order curvilinear simulations of flows around non-cartesian bodies”, J. Comput. Acoustics, 13:4 (2005), 731–748 | DOI | Zbl

[7] Henderson R. D., “Nonlinear dynamics and pattern formation in turbulent wake transition”, J. Fluid Mech., 352 (1997), 65–112 | DOI | MR | Zbl

[8] Zhang H., Fey U., Noack B. R. et al., “On the transition of the cylinder wake”, Phys. Fluids, 7:4 (1995), 779–794 | DOI

[9] Thompson M., Hourigan K., Sheridan J., “Three-dimensional instabilities in the wake of a circular cylinder”, Exp. Thermal Fluid Sci., 12:2 (1996), 190–196 | DOI

[10] Persillon A., Braza M., “Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation”, J. Fluid Mech., 365 (1998), 23–88 | DOI | Zbl

[11] Posdziech O., Grundmann R., “Numerical simulation of the flow around an infinitely long circular cylinder in the transition regime”, Theor. Comput. Fluid Dynamics, 15:2 (2001), 121–141 | DOI | Zbl

[12] Henderson R. D., “Details of the drag curve near the onset of vortex shedding”, Phys. Fluids, 7:9 (1995), 2102 | DOI