Geodesic
Method of adaptive artificial viscosity for the equations of gas dynamics on triangular and tetrahedral grids
Matematičeskoe modelirovanie, Tome 24 (2012) no. 6, pp. 109-127.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the papers [1–7] the adaptive artificial viscosity method (АAV) for solution of gas dynamics equations was proposed. In this paper this method is extended to the case of triangular grids for 2D case in $x$, $y$ and $r$, $z$ variables and tetrahedral grids for 3D in the Cartesian ones. Results of test computations are discussed.
Keywords: the method of adaptive artificial viscosity, equations of gas dynamics, unstructured grids. 
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I. V. Popov; I. V. Fryazinov. Method of adaptive artificial viscosity for the equations of gas dynamics on triangular and tetrahedral grids. Matematičeskoe modelirovanie, Tome 24 (2012) no. 6, pp. 109-127. http://geodesic.mathdoc.fr/item/MM_2012_24_6_a6/

[1] Popov I. V., Fryazinov I. V., “Setochnyi metod resheniya uravnenii gazovoi dinamiki s vvedeniem iskusstvennoi vyazkosti”, Setochnye metody dlya kraevykh zadach i prilozheniya, Materialy Sedmogo Vserossiiskogo seminara (21–24 sentyabrya 2007 g., g. Kazan, Rossiya), Izd-vo Kazanskogo gos. Universiteta, Kazan, 2007, 223–230

[2] Popov I. V., Fryazinov I. V., “Konechno-raznostnyi metod resheniya uravnenii gazovoi dinamiki s vvedeniem adaptivnoi iskusstvennoi vyazkosti”, Matematicheskoe modelirovanie, 20:8 (2008), 48–60 | MR

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

[4] Popov I. V., Fryazinov I. V., “Raschety dvumernykh testovykh zadach metodom adaptivnoi iskusstvennoi vyazkosti”, Matematicheskoe modelirovanie, 22:5 (2010), 57–66 | Zbl

[5] Popov I. V., Fryazinov I. V., “O metode adaptivnoi iskusstvennoi vyazkosti”, Matematicheskoe modelirovanie, 22:7 (2010), 121–128 | Zbl

[6] Popov I. V., Fryazinov I. V., “O novom vybore adaptivnoi iskusstvennoi vyazkosti”, Matematicheskoe modelirovanie, 22:12 (2010), 23–32 | Zbl

[7] Popov I. V., Fryazinov I. V., “Konechno-raznostnyi metod resheniya trekhmernykh uravnenii gazovoi dinamiki s vvedeniem adaptivnoi iskusstvennoi vyazkosti”, Matematicheskoe modelirovanie, 23:3 (2011), 89–100 | MR | Zbl

[8] Samarskii A. A., Koldoba A. V., Poveschenko Yu. A., Tishkin V. F., Favorskii A. P., Raznostnye skhemy na neregulyarnykh setkakh, Minsk, 1996, 273 pp.

[9] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1980, 352 pp. | MR

[10] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Nauka, M., 1968, 686 pp.

[11] Godunov S. K., Zabrodin A. V., Ivanov M. Ya., Kraiko A. N., Prokopov G. P., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976, 400 pp. | MR | Zbl

[12] Liska R., Wendroff B., “Comparison of several difference schemes on 1D and 2D test problems for the Euler equations”, SIAM J. Sci. Comput., 25:3 (2003), 995–1017 http://www.math.ntnu.no/conservation | DOI | MR | Zbl