Geodesic
Generalization of CABARET scheme for two-dimensional orthogonal computational grid
Matematičeskoe modelirovanie, Tome 25 (2013) no. 7, pp. 103-136.

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

CABARET scheme was generalized in two-dimensional case. The transition from one-dimensional problem to multidimensional connected with a number of new questions. The first one is spatial splitting procedure of flux variables. The another question connected with application of maximum principle for local invariant transport in different directions. Simulation test examples are given for each problem considered.
Mots-clés : CABARET
Keywords: conservative schemes. 
@article{MM_2013_25_7_a7,
     author = {V. M. Goloviznin and S. A. Karabasov and V. G. Kondakov},
     title = {Generalization of {CABARET} scheme for two-dimensional orthogonal computational grid},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {103--136},
     publisher = {mathdoc},
     volume = {25},
     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_7_a7/}
}
TY  - JOUR
AU  - V. M. Goloviznin
AU  - S. A. Karabasov
AU  - V. G. Kondakov
TI  - Generalization of CABARET scheme for two-dimensional orthogonal computational grid
JO  - Matematičeskoe modelirovanie
PY  - 2013
SP  - 103
EP  - 136
VL  - 25
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2013_25_7_a7/
LA  - ru
ID  - MM_2013_25_7_a7
ER  - 
%0 Journal Article
%A V. M. Goloviznin
%A S. A. Karabasov
%A V. G. Kondakov
%T Generalization of CABARET scheme for two-dimensional orthogonal computational grid
%J Matematičeskoe modelirovanie
%D 2013
%P 103-136
%V 25
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2013_25_7_a7/
%G ru
%F MM_2013_25_7_a7
V. M. Goloviznin; S. A. Karabasov; V. G. Kondakov. Generalization of CABARET scheme for two-dimensional orthogonal computational grid. Matematičeskoe modelirovanie, Tome 25 (2013) no. 7, pp. 103-136. http://geodesic.mathdoc.fr/item/MM_2013_25_7_a7/

[1] Goloviznin V. M., Samarskii A. A., “Raznostnaya approksimatsiya konvektivnogo perenosa s prostranstvennym rasschepleniem vremennoi proizvodnoi”, Matematicheskoe modelirovanie, 10:1 (1998), 86–100 | MR | Zbl

[2] Goloviznin V. M., Samarskii A. A., “Nekotorye svoistva raznostnoi skhemy KABARE”, Matematicheskoe modelirovanie, 10 (1998), 101–116 | MR | Zbl

[3] Goloviznin V. M., Karabasov S. A., “Nelineinaya korrektsiya skhemy «KABARE»”, Matematicheskoe modelirovanie, 12:1 (2000), 107–123 | MR

[4] Goloviznin V. M., Kanaev A. A., “Printsip minimuma partsialnykh lokalnykh variatsii dlya opredeleniya konvektivnykh potokov pri chislennom resheni odnomernykh nelineinykh skalyarnykh giperbolicheskikh uravnenii”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 51:5 (2011), 881–897 | MR | Zbl

[5] Goloviznin V. M., “Balansno-kharakteristicheskii metod chislennogo resheniya odnomernykh uravnenii gazovoi dinamiki v eilerovykh peremennykh”, Matematicheskoe modelirovanie, 18:11 (2006), 14–30 | MR | Zbl

[6] Goloviznin V. M., “Balansno-kharakteristicheskii metod chislennogo resheniya uravnenii gazovoi dinamiki”, Doklady Akademii Nauk, 403:4 (2005), 1–6 | MR

[7] Samarskii A. A., Popov Yu. P., Raznostnye metody resheniya zadach gazovoi dinamiki, Nauka, M., 1992 | MR

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

[9] Zhukov A. I., “Primenenie metoda kharakteristik k chislennomu resheniyu odnomernykh zadach gazovoi dinamiki”, Trudy Matematicheskogo instituta im. V. A. Steklova AN SSSR, 58, 1960, 3–150

[10] Magomedov K. M., Kholodov A. S., Setochno-kharakteristicheskie chislennye metody, Nauka, M., 1988 | MR

[11] Goloviznin V. M., Hynes T. P., Karabasov S. A., “CABARET finite-difference schemes for the one-dimensional Euler equations”, Mathematical Modelling and Analysis, 6:2 (2001), 210–220 | MR | Zbl

[12] Goloviznin V. M., Karabasov S. A., “Balansno-kharakteristicheskie skhemy na kusochno-postoyannykh nachalnykh dannykh. Pryzhkovyi perenos”, Matematicheskoe modelirovanie, 15:10 (2003), 71–83 | MR | Zbl

[13] Goloviznin V. M., Karabasov S. A., Kobrinskii I. M., “Balansno-kharakteristicheskie skhemy s razdelennymi konservativnymi i potokovymi peremennymi”, Matematicheskoe modelirovanie, 15:9 (2003), 29–48 | MR | Zbl

[14] Toro E. F., Titarev V. A., “Solution of the generalized Riemann problem for advection-reaction equations”, Proc. Roy. Soc., 458:2018 (2002), 271–281 | DOI | MR | Zbl

[15] Qiu J., Shu C.-W., “Hermite WENO schemes and their application as limiters for Runge–Kutta discontinuous Galerkin method: one dimensional case”, Journal of Computational Physics, 193 (2003), 115–135 | DOI | MR

[16] Garnier E., Sagaut P., Deville M., “A class of axplisit ENO filters with application to unsteady flows”, Journal of Computational Physics, 170 (2001), 184–204 | DOI | Zbl

[17] Zhou Y. C., Wei G. W., “High resolution conjugate filters for the simulation of flows”, Journal of Computational Physics, 189 (2003), 159–179 | DOI | MR | Zbl