Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 170-184 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Regularized shallow water equations are derived as based on a regularization of the Navier–Stokes equations in the form of quasi-gasdynamic and quasi-hydrodynamic equations. Efficient finite-difference algorithms based on the regularized shallow water equations are proposed for the numerical simulation of shallow water flows. The capabilities of the model are examined by computing a test Riemann problem, the flow over an obstacle, and asymmetric dam break.
@article{ZVMMF_2011_51_1_a12,
     author = {O. V. Bulatov and T. G. Elizarova},
     title = {Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {170--184},
     year = {2011},
     volume = {51},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a12/}
}
TY  - JOUR
AU  - O. V. Bulatov
AU  - T. G. Elizarova
TI  - Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 170
EP  - 184
VL  - 51
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a12/
LA  - ru
ID  - ZVMMF_2011_51_1_a12
ER  - 
%0 Journal Article
%A O. V. Bulatov
%A T. G. Elizarova
%T Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 170-184
%V 51
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a12/
%G ru
%F ZVMMF_2011_51_1_a12
O. V. Bulatov; T. G. Elizarova. Regularized shallow water equations and an efficient method for numerical simulation of shallow water flows. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 1, pp. 170-184. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_1_a12/

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

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

[3] Sheretov Yu. V., Dinamika sploshnykh sred pri prostranstvenno-vremennom osrednenii, M., Izhevsk, 2009

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

[5] Sretenskii N. L., Teoriya volnovykh dvizhenii zhidkosti, Nauka, M., 1977

[6] Landau L. D., Lifshits E. M., Gidrodinamika, Nauka, M., 1986 | MR

[7] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii, Mir, M., 1978

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

[9] Sheretov Yu. V., “O svoistvakh reshenii kvazigidrodinamicheskikh uravnenii v barotropnom priblizhenii”, Vestn. Tverskogo gos. un-ta. Ser. prikl. matem., 2009, no. 3, 5–19

[10] Zlotnik A. A., Chetverushkin B. N., “Parabolicity of the quasi-gasdynamic system of equations, its hyperbolic second-order modification, and the stability of small perturbations for them”, Comput. Math. and Math. Phys., 48:3 (2008), 420–446 | DOI | MR | Zbl

[11] Zlotnik A. A., “Energeticheskie ravenstva i otsenki dlya barotropnykh kvazigazo- i kvazigidrodinamicheskikh sistem uravnenii”, Zh. vychisl. matem. i matem. fiz., 50:2 (2010), 325–337 | MR

[12] Elizarova T. G., Afanaseva M. V., “Regulyarizovannye uravneniya melkoi vody”, Vestn. MGU. Ser. 3. Fizika. Astronomiya, 2010, no. 1, 15–18

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

[14] Kun Xu, “A well-balanced gas-kinetic scheme for the shallow-water equations with source terms”, J. Comput. Phys., 178 (2002), 533–562 | DOI | MR | Zbl

[15] Noelle S., Pankratz N., Puppo G., Natvig J. R., “Well-balances finite volume schemes of arbitrary order of accuracy for shallow water flows”, J. Comput. Phys., 213 (2006), 474–499 | DOI | MR | Zbl

[16] Birman A., Falcovitz J., “Application of the GRP scheme to open channel flow equations”, J. Comput. Phys., 222 (2007), 131–154 | DOI | MR | Zbl

[17] Glaster P., “The efficient prediction of shallow water flows. Part II: Application”, Comput. Math. Applic., 33:9 (1997), 115–148 | DOI | MR

[18] Ricchiuto M., Abgarall R., Deconinck H., “Application of conservative residual distribution schemes to the solution of the shallow water equations on unstructured meshes”, J. Comput. Phys., 222 (2007), 287–331 | DOI | MR | Zbl