Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1142-1160 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The CABARET scheme is used for the numerical solution of the one-dimensional shallow water equations over a rough bottom. The scheme involves conservative and flux variables, whose values at a new time level are calculated by applying the characteristic properties of the shallow water equations. The scheme is verified using a series of test and model problems.
@article{ZVMMF_2017_57_7_a5,
     author = {V. M. Goloviznin and V. A. Isakov},
     title = {Balance-characteristic scheme as applied to the shallow water equations over a rough bottom},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1142--1160},
     year = {2017},
     volume = {57},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/}
}
TY  - JOUR
AU  - V. M. Goloviznin
AU  - V. A. Isakov
TI  - Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 1142
EP  - 1160
VL  - 57
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/
LA  - ru
ID  - ZVMMF_2017_57_7_a5
ER  - 
%0 Journal Article
%A V. M. Goloviznin
%A V. A. Isakov
%T Balance-characteristic scheme as applied to the shallow water equations over a rough bottom
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 1142-1160
%V 57
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/
%G ru
%F ZVMMF_2017_57_7_a5
V. M. Goloviznin; V. A. Isakov. Balance-characteristic scheme as applied to the shallow water equations over a rough bottom. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 7, pp. 1142-1160. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_7_a5/

[1] Glaister P., “Approximate Riemann solutions of the shallow water equations”, ASCE J. Hydraulic Engng., 26:3 (1988), 293–306 | MR

[2] Garcia-Navarro P., Vazquez M. E., “On numerical treatment of the source terms in shallow water equations”, Comput. Fluids, 29 (2000), 951–979 | DOI | Zbl

[3] Toro E. F., Shock-capturing methods for free-surface shallow flows, Wiliey, New York, 2001 | Zbl

[4] Yuxin H., Ningchuan Z., Yuguo P., “Well-balanced finite volume scheme for shallow water flooding and drying over arbitrary topography”, Eng. Appl. Comput. Fluid Mech., 7:1 (2013), 40–54

[5] Harnet E., Le Roux D. Y., Legat V., Deleersnijder E., “An efficient Eulerian finite element method for the shallow water equations”, Ocean Modelling, 10 (2005), 115–136 | DOI

[6] Heniche M., Secretan Y., Boundreau P., Leclerc M., “A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries”, Advances in Water Resource, 23 (2000), 359–372 | DOI

[7] Goloviznin V. M., Karabasov S. A., “Balansno-kharakteristicheskie skhemy s razdelennymi konservativnymi i potokovymi peremennymi”, Matem. modelirovanie, 15:9 (1998), 29–48

[8] Goloviznin V. M., Karabasov S. A., “Nelineinaya korrektsiya skhemy “Kabare””, Matem. modelirovanie, 10:12 (1998), 107–123

[9] Harten A., “High Resolution Schemes for Hyperbolic Conservation Laws”, J. of Comput. Phys., 49:3 (1983), 357–393 | DOI | MR | Zbl

[10] Goloviznin V. M., Zaitsev M. A., Karabasov S. A., Korotkin I. A., Novye algoritmy vychislitelnoi gidrodinamiki dlya mnogoprotsessornykh vychislitelnykh kompleksov, Izd-vo MGU, M., 2013

[11] Ostapenko V. V., “O monotonnosti balansno-kharakteristicheskoi skhemy”, Matem. modelirovanie, 21:7 (2009), 29–42 | Zbl

[12] Kovyrkina O. A., Ostapenko V. V., “O monotonnosti dvukhsloinoi po vremeni skhemy kabare”, Matem. modelirovanie, 24:9 (2012), 97–112

[13] Zyuzina N. A., Ostapenko V. V., “O monotonnosti skhemy KABARE, approksimiruyuschei skalyarnyi zakon sokhraneniya s vypuklym potokom”, Dokl. AN, 466:5 (2016), 513–517 | DOI | Zbl

[14] Petrosyan A. S., Dopolnitelnye glavy teorii melkoi vody, Rotaprint IKI RAN, M., 2014, 64 pp.

[15] Ostapenko V. V., “Techeniya, voznikayuschie pri razrushenii plotiny nad ustupom dna”, PMTF, 44:6 (2003), 107–122 | Zbl

[16] Ostapenko V. V., “Techeniya, voznikayuschie pri razrushenii plotiny nad stupenkoi dna”, PMTF, 44:4 (2003), 51–63

[17] Bernetti R., Titarev V. A., Toro E. F., “Exact solution of the Riemann problem for the shallow water equations with discontinuous bottom geometry”, J. Comput. Phys., 227 (2008), 3212–3243 | DOI | MR | Zbl

[18] Petrosyan A. S., Dopolnitelnye glavy gidrodinamiki tyazheloi zhidkosti so svobodnoi granitsei, Rotaprint IKI RAN, M., 2010, 65 pp.

[19] Toro E. F., “Riemann problems and the WAF Method for solving the two dimensional shallow water equations”, Phil. Trans. R. Soc. Lond. A, 338 (1992), 43–68 | DOI | MR | Zbl