Capabilities of a quasi-gasdynamic algorithm as applied to inviscid gas flow simulation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 549-566 Cet article a éte moissonné depuis la source Math-Net.Ru

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Ten well-known one-dimensional test problems reflecting the characteristic features of unsteady inviscid gas flows are successfully solved by a unified numerical algorithm based on the quasigasdynamic system of equations. In all the cases, the numerical solution converges to a self-similar one as the spatial grid is refined.
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T. G. Elizarova; E. V. Shilnikov. Capabilities of a quasi-gasdynamic algorithm as applied to inviscid gas flow simulation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 3, pp. 549-566. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_3_a13/

[1] Rozhdestvenskii B. L., Yanenko H. H., Sistemy kvazilineinykh uravnenii, Nauka, M., 1978

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

[3] Liska R., Wendroff B., Comparison of several difference schemes on ID and 2D test problems for Euler equations, Techn. Rept LA-UR-01-6225, LANL, Los Alamos, 2001

[4] Liska R., Wendroff B., “Comparison of several difference schemes on ID and 2D test problems for the Euler equations”, SIAM J. Sci. Comput., 25:3 (2003), 995–1017 | DOI | MR | Zbl

[5] Sheretov Yu. V., Matematicheskoe modelirovanie techenii zhidkosti i gaza na osnove kvazigidrodinamicheskikh i kvazigazodinamicheskikh uravnenii, Tverskoi gos. un-t, Tver, 2000

[6] Elizarova T. G., Sokolova M. E., Sheretov Yu. V., “Kvazigazodinamicheskie uravneniya i chislennoe modelirovanie techenii vyazkogo gaza. II”, Zh. vychisl. matem. i matem. fiz., 45:3 (2005), 545–556 | MR

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

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

[9] Toro E., Rieman solvers and numerical methods for fluid dynamics, Springer, Berlin–Heidelberg, 1997 | MR

[10] Graur I. A., “Raznostnye skhemy rasschepleniya dlya resheniya uravnenii Eilera, postroennye na osnove kvazigazodinamicheskikh uravnenii”, Zh. vychisl. matem. i matem. fiz., 44:1 (2004), 166–178 | MR | Zbl

[11] Noh W. F., “Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux”, J. Comput. Phys., 72 (1987), 78–120 | DOI | Zbl

[12] Shu C., Osher S., “Effecient implementation of essentially non-oscillatory shook-capturing schemes. II”, J. Comput. Phys., 83 (1989), 32–78 | DOI | MR | Zbl

[13] Kudryavtsev A. H., Poplavskaya T. V., Khotyanovskii D. V., “Primenenie skhem povyshennogo poryadka tochnosti pri modelirovanii nestatsionarnykh sverkhzvukovykh techenii”, Matem. modelirovanie, 19:7 (2007), 39–55 | MR | Zbl

[14] Woodward P., Colella P., “The numerical simulation of two-dimensional fluid flow with strong shocks”, J. Comput. Phys., 54 (1984), 115–173 | DOI | MR | Zbl

[15] Breslavskii P. V., Mazhukin V. I., “Modelirovanie vzaimodeistviya udarnykh voln na dinamicheski adaptiruyuschikhsya setkakh”, Matem. modelirovanie, 19:11 (2007), 83–95 | MR