Geodesic
Numerical method of hydromechanics equations in multiply connected domains
Matematičeskoe modelirovanie, Tome 18 (2006) no. 12, pp. 3-18.

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

Multiply-connected domains (MDs) have been considered. For solving hydrodynamics equations in these three-dimensional domains with curvlinear boundary surfaces, it is proposed to divide MDs by the totality of final volumes (FV) belonging to three types. FVs of two types are simply-connected, and the FVs of the third type are biconnected. In the general case, the FVs also have curvilinear bounding surfaces, which are spatial formations serving as a basis for carrying out the parallelization of a computational process. For the solution of hydrodynamics equations, the difference scheme is unwound for the simply-connected FVs. In the biconnected FVs, the approximate solution is found in the form of polynomials for the given totality of computation points. The initial and boundary conditions are formulated for the general MD. In order to obtain a continuous solution, the conjugation conditions of the appropriate order being defined by the accuracy of the approximated solution are imposed when passing from one FV to another. It is shown that when the above conditions are fulfilled, the magnitudes of hydromechanical parameters in multiply-connected domains are calculated in the same way as in the simply-connected domains. 
@article{MM_2006_18_12_a0,
     author = {A. M. Lipanov},
     title = {Numerical method of hydromechanics equations in multiply connected domains},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {18},
     number = {12},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_12_a0/}
}
TY  - JOUR
AU  - A. M. Lipanov
TI  - Numerical method of hydromechanics equations in multiply connected domains
JO  - Matematičeskoe modelirovanie
PY  - 2006
SP  - 3
EP  - 18
VL  - 18
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2006_18_12_a0/
LA  - ru
ID  - MM_2006_18_12_a0
ER  - 
%0 Journal Article
%A A. M. Lipanov
%T Numerical method of hydromechanics equations in multiply connected domains
%J Matematičeskoe modelirovanie
%D 2006
%P 3-18
%V 18
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2006_18_12_a0/
%G ru
%F MM_2006_18_12_a0
A. M. Lipanov. Numerical method of hydromechanics equations in multiply connected domains. Matematičeskoe modelirovanie, Tome 18 (2006) no. 12, pp. 3-18. http://geodesic.mathdoc.fr/item/MM_2006_18_12_a0/

[1] Bulgakov V. K., Kodolov V. I., Lipanov A. M., Modelirovanie goreniya polimernykh materialov, Khimiya, M., 1990

[2] Gallager R., Metod konechnykh elementov. Osnovy, Mir, M., 1984 | MR

[3] Gorokhov M. M., Rusyak I. G., Tenenev V. A., “Chislennoe issledovanie goreniya chastits alyuminiya v dvukhfaznom potoke”, Matem. modelirovanie, 9:5 (1997), 87–96 | Zbl

[4] Lipanov A. M., Kisarov Yu. F., Klyuchnikov I. G., Chislennyi eksperiment v klassicheskoi gidromekhanike turbulentnykh potokov, Izdatelstvo Prezidiuma UrO RAN, Ekaterinburg, 2001

[5] Bronshtein I. N., Semendyaev K. A., Spravochnik po vysshei matematike, Nauka, M., 1986

[6] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, Ch. II, Fizmatgiz, M., 1968

[7] Fedorchenko A. T., “O probleme vyvoda vikhrei cherez pronitsaemuyu granitsu raschetnoi oblasti nestatsionarnogo dozvukovogo potoka”, ZhVM i MF, 26:1 (1986), 114–129 | MR | Zbl

[8] Rozhdestvenskii B. L., Simakin I. N., “Modelirovanie turbulentnykh techenii v ploskom kanale”, ZhVM i MF, 25:1 (1985), 96–121 | MR | Zbl

[9] Zalesak S. T., “A Physical Interpretation of the Richtmyer two-step Lax-Wendroff scheme, and its generalization to higher spatial order”, Advances in Computer Methods for Partial Differential Equations, IMACS, 1984, 491–496

[10] Samarskii A. A., Vabischevich P. N., Matus P. P., Raznostnye skhemy s operatornymi mnozhitelyami, ZAO “TsOTZh”, Minsk, 1998

[11] Sorkin R. E., Vnutrikamernye protsessy v raketnykh sistemakh na tverdom toplive, Nauka, M., 1983