Geodesic
Numerical Simulation of Shallow Water Flows on the Rotating Attractive Sphere
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 30-45

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

We derive system conservation of laws for the equations of shallow water on the rotating attractive sphere (mass and total momentum). We construct exact stationary solution with a step profile of depth. These solutions are used for testing explicit two-layer on time difference scheme. We spent numerical simulation of evolution one-dimensional non-stationary discontinuous waves on rotating attractive sphere.
Keywords: conservation laws for shallow water equations on a rotating attractive sphere, discontinuous flow of boron type on a sphere, difference scheme, numerical simulation. 
A. V. Ivanova; V. V. Ostapenko; A. P. Chupakhin. Numerical Simulation of Shallow Water Flows on the Rotating Attractive Sphere. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 3, pp. 30-45. http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a2/
@article{VNGU_2010_10_3_a2,
     author = {A. V. Ivanova and V. V. Ostapenko and A. P. Chupakhin},
     title = {Numerical {Simulation} of {Shallow} {Water} {Flows} on the {Rotating} {Attractive} {Sphere}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {30--45},
     year = {2010},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a2/}
}
TY  - JOUR
AU  - A. V. Ivanova
AU  - V. V. Ostapenko
AU  - A. P. Chupakhin
TI  - Numerical Simulation of Shallow Water Flows on the Rotating Attractive Sphere
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2010
SP  - 30
EP  - 45
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a2/
LA  - ru
ID  - VNGU_2010_10_3_a2
ER  - 
%0 Journal Article
%A A. V. Ivanova
%A V. V. Ostapenko
%A A. P. Chupakhin
%T Numerical Simulation of Shallow Water Flows on the Rotating Attractive Sphere
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2010
%P 30-45
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/VNGU_2010_10_3_a2/
%G ru
%F VNGU_2010_10_3_a2

[1] Stoker Dzh. Dzh., Volny na vode, Izd-vo inostr. lit., M., 1959

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

[3] Pedloski Dzh., Geofizicheskaya gidrodinamika, v. 1, 2, Mir, M., 1984

[4] Diikstra Kh., Nelineinaya fizicheskaya okeanografiya, NITs Regulyarnaya i khaoticheskaya dinamika, Institut kompyuternykh issledovanii, M.–Izhevsk, 2007

[5] Cherevko A. A., Chupakhin A. P., “Uravneniya modeli melkoi vody na vraschayuscheisya prityagivayuschei sfere. 1: Vyvod i obschie svoistva”, PMTF, 50:2 (2009), 37–45 | MR

[6] Cherevko A. A., Chupakhin A. P., “Uravneniya modeli melkoi vody na vraschayuscheisya prityagivayuschei sfere. 2: Prostye statsionarnye volny i zvukovye kharakteristiki”, PMTF, 50:3 (2009), 82–96 | MR

[7] Ostapenko V. V., Giperbolicheskie sistemy zakonov sokhraneniya i ikh prilozhenie k teorii melkoi vody, Novosibirsk, 2004

[8] Schacht W., Vorozhtsov E. V., Voevodin A. F., Ostapenko V. V., “Numerical Modeling of Hydraulic Jumps in a Spiral Channel with Rectangular Cross Section”, Fluid Dynamic Res., 31 (2002), 185–213 | DOI

[9] Marchuk G. I., Metody rasschepleniya, Nauka, M., 1988 | MR

[10] Ostapenko V. V., “O skhodimosti raznostnykh skhem za frontom nestatsionarnoi udarnoi volny”, Zhurn. vych. mat. i mat. fiz., 37:10 (1997), 1201–1212 | MR | Zbl

[11] Casper J., Carpenter M. N., “Computational Consideration for the Simulation of Shock-Induced Sound”, SIAM J. Sci. Comput., 19:1 (1998) | MR | Zbl

[12] Stanyukovich K. P., Neustanovivshiesya dvizheniya sploshnoi sredy, Nauka, M., 1971 | MR

[13] Patterson W., “A New Record of Climate Variability from Northern Labrador Revealed from Isotope Chemistry of Tree Rings”, Proc. Int. Conf. BOREAS (Rovaniemi, Finland, 28–31 October 2009), Invited