Geodesic
The solution of gas dynamics problems with shock waves using Runge--Kutta discontinous Galerkin method
Matematičeskoe modelirovanie, Tome 20 (2008) no. 11, pp. 55-66.

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

The paper is dedicated to the testing of RKDG method for gas dynamics and to the comparison of this method with other well-known numerical methods. The comparative analysis was carried out between different variants of RKDG method as well as finite-volume Godunov type schemes. The computations allow to estimate the quality of different schemes. RKDG method has a higher order of approximation, which leads to better quality of the solution. 
@article{MM_2008_20_11_a4,
     author = {M. P. Galanin and E. B. Savenkov and S. A. Tokareva},
     title = {The solution of gas dynamics problems with shock waves using {Runge--Kutta} discontinous {Galerkin} method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {55--66},
     publisher = {mathdoc},
     volume = {20},
     number = {11},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_11_a4/}
}
TY  - JOUR
AU  - M. P. Galanin
AU  - E. B. Savenkov
AU  - S. A. Tokareva
TI  - The solution of gas dynamics problems with shock waves using Runge--Kutta discontinous Galerkin method
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 55
EP  - 66
VL  - 20
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_11_a4/
LA  - ru
ID  - MM_2008_20_11_a4
ER  - 
%0 Journal Article
%A M. P. Galanin
%A E. B. Savenkov
%A S. A. Tokareva
%T The solution of gas dynamics problems with shock waves using Runge--Kutta discontinous Galerkin method
%J Matematičeskoe modelirovanie
%D 2008
%P 55-66
%V 20
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_11_a4/
%G ru
%F MM_2008_20_11_a4
M. P. Galanin; E. B. Savenkov; S. A. Tokareva. The solution of gas dynamics problems with shock waves using Runge--Kutta discontinous Galerkin method. Matematičeskoe modelirovanie, Tome 20 (2008) no. 11, pp. 55-66. http://geodesic.mathdoc.fr/item/MM_2008_20_11_a4/

[1] Bernardo Cockburn, Chi-Wang Shu, “Runge–Kutta discontinuous Galerkin methods for convection-dominated problems”, Journal of Scientific Computing, 16:3 (2001), 173–261 | DOI | MR | Zbl

[2] Galanin M. P., Savenkov E. B., Tokareva S. A., Primenenie razryvnogo metoda Galerkina dlya chislennogo resheniya kvazilineinogo uravneniya perenosa, Preprint No 105, IPM im. M. V. Keldysha RAN, 2005, 35 pp.

[3] Galanin M. P., Grischenko E. V., Savenkov E. B., Tokareva S. A., Primenenie RKDG metoda dlya chislennogo resheniya zadach gazovoi dinamiki, Preprint No 52, IPM im. M. V. Keldysha RAN, 2006, 31 pp.

[4] Kulikovskii A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii, Fizmatlit, M., 2001, 608 pp. | MR | Zbl

[5] Toro E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics. A Practical Introduction, Springer, Berlin, 1999, 624 pp. | MR

[6] Kuznetsov O. A., Matematicheskoe modelirovanie dvoinykh zvezdnykh sistem, Dis. d.f.-m.n., M., 1999, 323 pp.

[7] Woodward P., Colella P., “The numerical simulation of two-dimensional fluid flow with strong shocks”, Journal of Computational Physics, 54 (1984), 115 | DOI | MR | Zbl

[8] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Editorial URSS, M., 2004, 424 pp.

[9] Chzhen P. K., Otryvnye techeniya, t. 1, Mir, M., 1972, 299 pp.; т. 2, 1973, 279 с.; т. 3, 1973, 333 с.

[10] Krasnov N. F., Koshevoi V. N., Kalugin V. T., Aerodinamika otryvnykh techenii, Vysshaya shkola, M., 1988, 351 pp.

[11] Krasnov N. F., Koshevoi V. N., Danilov A. N. i dr., Prikladnaya aerodinamika, Vysshaya shkola, M., 1974, 731 pp.

[12] Krasnov N. F., Koshevoi V. N., Zakharchenko V. F., Danilov A. I., Osnovy prikladnoi aerodinamiki. Kn. 2. Obtekanie tel vyazkoi zhidkostyu. Rulevye ustroistva, Vysshaya shkola, M., 1991, 351 pp.

[13] Deich M. E., Tekhnicheskaya gazodinamika (osnovy gazodinamiki turbin), Energoizdat, M.-L., 1953, 544 pp.

[14] Loitsyanskii L. G., Mekhanika zhidkosti i gaza, Drofa, M., 2003, 840 pp.