Geodesic
Numerical Simulation of Interaction Solitary Wave with Underwater Step by Natural Element Method
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 67-73 
S. N. Karabtcev; S. V. Stukolov. Numerical Simulation of Interaction Solitary Wave with Underwater Step by Natural Element Method. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 2, pp. 67-73. http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a5/
@article{VNGU_2008_8_2_a5,
     author = {S. N. Karabtcev and S. V. Stukolov},
     title = {Numerical {Simulation} of {Interaction} {Solitary} {Wave} with {Underwater} {Step} by {Natural} {Element} {Method}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {67--73},
     year = {2008},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a5/}
}
TY  - JOUR
AU  - S. N. Karabtcev
AU  - S. V. Stukolov
TI  - Numerical Simulation of Interaction Solitary Wave with Underwater Step by Natural Element Method
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2008
SP  - 67
EP  - 73
VL  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a5/
LA  - ru
ID  - VNGU_2008_8_2_a5
ER  - 
%0 Journal Article
%A S. N. Karabtcev
%A S. V. Stukolov
%T Numerical Simulation of Interaction Solitary Wave with Underwater Step by Natural Element Method
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2008
%P 67-73
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/VNGU_2008_8_2_a5/
%G ru
%F VNGU_2008_8_2_a5

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

In present work results of numerical modeling of a problem about movement of a solitary wave above a underwater obstacle as a rectangular step are submitted. The solving of the given problem is carried out by a natural element method within the framework of model of an ideal incompressible fluid on the basis of system of the equations of Euler. Formation of vortexes near to a step is revealed, and also influence of vortexes on amplitudes of the past and reflected waves is established.

[1] Afanasev K. E., Reshenie nelineinykh zadach gidrodinamiki idealnoi neszhimaemoi zhidkosti so svobodnymi granitsami metodami konechnykh i granichnykh elementov, Avtoref. dis. ... d-ra fiz.-mat. nauk, Kemerovo, 1997

[2] Afanasev K. E., Karabtsev S. N., Rein T. S. i dr., “Metod estestvennykh sosedei na osnove interpolyatsii Sibsona”, Vest. Tom. gos. un-ta. Seriya: Matematika. Kibernetika. Informatika. Vyp. «Informatsionnye tekhnologii i matematicheskoe modelirovanie», 2006, no. 19, 210–219

[3] Karabtsev S. N., Stukolov S. V., “Effektivnyi algoritm generatsii konechnoelementnoi setki dlya metoda estestvennykh sosedei”, Gidrodinamika bolshikh skorostei i chislennoe modelirovanie, Materialy III mezhdunar. nauch. letnei shkoly, INT, Kemerovo, 2006, 401–409

[4] Stukolov S. V., Reshenie nelineinykh volnovykh zadach gidrodinamiki idealnoi zhidkosti kompleksnym metodom granichnykh elementov, Avtoref. dis. \ldots kand. fiz.-mat. nauk, Kemerovo, 1999

[5] Frank A. M., Diskretnye modeli neszhimaemoi zhidkosti, Fizmatlit, M., 2001

[6] Khazhoyan M. G., Khakimzyanov G. S., “Chislennoe modelirovanie vzaimodeistviya poverkhnostnykh voln s podvodnymi prepyatstviyami”, Vych. tekhnologii, 8:4 (2003), 108–123 | Zbl

[7] Shokin Yu. I., Ruziev R. A., Khakimzyanov G. S., Chislennoe modelirovanie ploskikh potentsialnykh techenii zhidkosti s poverkhnostnymi volnami, Prepr. No 12, Vychislitelnyi tsentr SO AN SSSR, Krasnoyarsk, 1990

[8] Yanenko N. N., “Ob ekonomichnykh neyavnykh skhemakh (metod drobnykh shagov)”, DAN SSSR, 134 (1960)

[9] Liu G. R., Mesh Free Methods: Moving Beyond the Finite Element Method, CRC Press, L., 2003 | MR

[10] Seabra-Santos F. J., Renouard D. P., Temperville A. M., “Numerical and Experimental Study of the Transformation of a Solitary Wave over a Shelf or Isolated Obstacle”, J. Fluid Mech., 176 (1987), 117–134 | DOI

[11] Sukumar N., Moran B., Belytschko T., “The Natural Element Method in Solid Mechanics”, Int. J. Num. Methods Eng., 43:5 (1998), 839–887 | 3.0.CO;2-R class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl