Geodesic
Method of adaptive artificial viscosity for solving the Navier–Stokes equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1356-1362 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical technique based on the method of adaptive artificial viscosity is proposed for solving the viscous compressible Navier–Stokes equations in two dimensions. The Navier–Stokes equations is approximated on unstructured meshes, namely, on triangular or tetrahedral elements. The monotonicity of the difference scheme according to the Friedrichs criterion is achieved by adding terms with adaptive artificial viscosity to the scheme. The adaptive artificial viscosity is determined by satisfying the maximum principle conditions. An external flow around a cylinder at various Reynolds numbers is computed as a numerical experiment. 
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I. V. Popov; I. V. Fryazinov. Method of adaptive artificial viscosity for solving the Navier–Stokes equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 8, pp. 1356-1362. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_8_a7/

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[2] Popov I. V., Fryazinov I. V., “Adaptivnaya iskusstvennaya vyazkost dlya mnogomernoi gazovoi dinamiki v eilerovykh peremennykh v dekartovykh koordinatakh”, Matem. modelirovanie, 22:1 (2010), 32–45

[3] Popov I. V., Fryazinov I. V., “Metod adaptivnoi iskusstvennoi vyazkosti dlya uravnenii gazovoi dinamiki na treugolnykh i tetraedralnykh setkakh”, Matem. modelirovanie, 24:6 (2012), 109–127 | Zbl

[4] Popov I. V., Fryazinov I. V., Metod adaptivnoi iskusstvennoi vyazkosti chislennogo resheniya uravnenii gazovoi dinamiki, Krasand, M., 2014

[5] Popov I. V., Fryazinov I. V., “Konechno-raznostnyi metod resheniya dvumernykh uravnenii Nave–Stoksa s adaptivnoi iskusstvennoi vyazkostyu”, Materialy Desyatoi mezhdunarodnoi konferentsii “Setochnye metody dlya kraevykh zadach i prilozheniya”, Kazanskii universitet, Kazan, 2014, 503–509