Geodesic
Adaptive artificial viscosity for gas dynamics for the Euler variables in Cartesian coordinates
Matematičeskoe modelirovanie, Tome 22 (2010) no. 1, pp. 32-45.

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It is considered a method of adaptive artificial viscosity (АAV2D-3D) of decision for two- and three-dimensional equations of gas dynamics for the Euler variables in the Cartesian coordinates system. This paper continues the works [1], [2]. The computational scheme is described in detail, and the results of test case are given. 
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I. V. Popov; I. V. Fryazinov. Adaptive artificial viscosity for gas dynamics for the Euler variables in Cartesian coordinates. Matematičeskoe modelirovanie, Tome 22 (2010) no. 1, pp. 32-45. http://geodesic.mathdoc.fr/item/MM_2010_22_1_a2/

[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 | Zbl

[3] Godunov S. K., Zabrodin A. V., Ivanov M. Ya., Prokopov G. P. i dr., Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki, Nauka, M., 1976 | MR | Zbl

[4] Chetverushkin B. N., Kineticheskie skhemy i kvazigazodinamicheskaya sistema uravnenii, Maks-Press, M., 2004

[5] Elizarova T. G., Kvazigazodinamicheskie uravneniya i metody rascheta vyazkikh techenii, Nauchnyi mir, M., 2007

[6] Kulikovskii A. G., Pogorelov N. V., Semënov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh uravnenii, Fizmatlit, M., 2001

[7] Liska Richard, Wendroff Burton, “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

[8] Vasilevskii V. F., Vyaznikov K. V., Tishkin V. F., Favorskii A. P., Kvazimonotonnye raznostnye skhemy povyshennogo poryadka tochnosti na adaptivnykh setkakh neregulyarnoi struktury, preprint No 124, IPM im. M. V. Keldysha AN SSSR, M., 1990

[9] Holden H., Lie K.-A., Risebro N. H., An unconditionally stable method for the Euler equations, Preprint 1998-018 | MR

[10] Toro E. F., Riemann solvers and numerical methods for fluid dynamics. A practical introduction, Springer, 1999 | MR