Sufficient conditions of stability in calculations of stationary supersonic flows by a marching method and non-stationary viscous flows
Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 93-104.

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In this paper the sufficient conditions of stability and monotony are received for calculations of supersonic stationary flows by a marching method. The sufficient conditions of stability are established also when constructing the explicit numerical schemes for solutions of non-stationary conservation lows with viscosity taken into account. The received conditions continuously transfer from a hyperbolic type of time step restrictions to parabolic ones as the viscosity coefficient increases.
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V. G. Grudnitskii. Sufficient conditions of stability in calculations of stationary supersonic flows by a marching method and non-stationary viscous flows. Matematičeskoe modelirovanie, Tome 20 (2008) no. 2, pp. 93-104. http://geodesic.mathdoc.fr/item/MM_2008_20_2_a8/

[1] V. G. Grudnitskii, “Obobschënnye kharakteristiki dlya sistemy uravnenii Eilera i ikh primenenie k konstruirovaniyu chislennykh skhem”, Matem. modelirovanie, 4:12 (1992), 45–48

[2] V. G. Grudnitskii, “Obobschënnye kharakteristiki dlya sistemy uravnenii Eilera”, Algoritmy dlya chislennogo issledovaniya razryvnykh techenii, VTs RAN, 1993, 191–203 | MR

[3] V. G. Grudnitskii, “Obobschënnye kharakteristiki i dostatochnoe uslovie ustoichivosti dlya uravnenii Eilera s razryvnymi resheniyami”, Matem. modelirovanie, 9:12 (1997), 121–125 | MR

[4] V. G. Grudnitskii, “Dostatochnoe uslovie ustoichivosti pri yavnom postroenii razryvnykh reshenii sistemy uravnenii Eilera”, DAN, 362:3 (1998), 298–299 | MR

[5] V. G. Grudnitskii, “Dostatochnoe uslovie ustoichivosti mnogomernogo raschëta nestatsionarnykh razryvnykh reshenii uravnenii Eilera”, Matem. modelirovanie, 12:1 (2000), 65–77 | MR

[6] V. G. Grudnitskii, P. V. Plotnikov, “Obobschënnye kharakteristiki i dostatochnoe uslovie ustoichivosti pri postroenii razryvnykh reshenii sistemy uravnenii Eilera”, Novoe v chislennom modelirovanii, 2000, 148–164 | MR

[7] V. G. Grudnitskiy, “Sufficient conditions of stability for discontinuous solutions of the Euler equations”, Computational Fluid Dynamics J., 10:2 (2001), 334–337

[8] V. G. Grudnitskii, “Pryamoi obobschënno-kharakteristicheskii metod dlya raschëta razryvnykh reshenii zakonov sokhraneniya gazovoi dinamiki”, Matem. modelirovanie, 16:1 (2004), 90–96 | Zbl

[9] V. G. Grudnitskii, “O dostatochnykh usloviyakh ustoichivosti dlya skhemy S. K. Godunova”, Matem. modelirovanie, 17:12 (2005), 119–128 | MR

[10] V. G. Grudnitskii, “Dostatochnye usloviya ustoichivosti pri raschëte razryvnykh reshenii nestatsionarnykh zakonov sokhraneniya v krivolineinykh koordinatakh i pri nalichii pravykh chastei”, Matem. modelirovanie, 18:10 (2006), 76–80

[11] P. D. Lax, “Weak solutions of nonlinear hyperbolic equations and their numerical computation”, Com. Pure and Appl. Math., 7 (1954), 159–193 | DOI | MR | Zbl

[12] S. K. Godunov, “Raznostnyi metod raschëta udarnoi volny”, UMN, 12:1 (1957), 176–177 | MR | Zbl

[13] V. S. Ryabenkii, A. F. Filippov, Ob ustoichivosti raznostnykh uravnenii, Gostekhizdat, M., 1956