Geodesic
New method for three-dimensional convection on large grids
Matematičeskoe modelirovanie, Tome 15 (2003) no. 6, pp. 53-58 
V. P. Ginkin; S. M. Ganina. New method for three-dimensional convection on large grids. Matematičeskoe modelirovanie, Tome 15 (2003) no. 6, pp. 53-58. http://geodesic.mathdoc.fr/item/MM_2003_15_6_a9/
@article{MM_2003_15_6_a9,
     author = {V. P. Ginkin and S. M. Ganina},
     title = {New method for three-dimensional convection on large grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {53--58},
     year = {2003},
     volume = {15},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2003_15_6_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In the present work the method of solution of three-dimensional hydrodynamic equations in Bussinesq approach is presented. The finite-difference method is used for spatial derivative and implicit method is used for time derivative. Global nonlinear system of equations is linearized and solved by the stabilization method at each time step. To solve the linearized equations of convectional heat-mass transfer we apply the method using exponential transformation and the conjugate gradient method with preconditioning by the incomplete factorisation method.

[1] Ginkin V., “Methods of solution of convective heat mass transfer at single crystal growth problem”, Proceedings of 2-nd Int. Symp. on Advances in Computational Heat Transfer (Palm Cove, Queensland, Australia, 20–25 May, 2001)

[2] Patankar S. V., Spalding D. B., “A Calculation procedure for heat, mass and momentum transfer in threedimensional parabolic flows”, J. Heat Mass Transfer, 15 (1972), 1787–1806 | DOI | Zbl

[3] Artemiev V. K., “An implicit method for a solution of the Navier–Stokes equations in natural variables”, Modeling in Mechanics, 6(23):1 (1992), 17

[4] Ginkin V. P., Kulik A. V., Naumenko O. M., “An efficient preconditioning procedure in the conjugate gradient method for 3D HEX-Z geometry”, Proceedings of 4-th Int. Conf. on Supercomputing in Nuclear Computations (SNA 2000) (Tokyo, Japan, 2000)

[5] Bessonov O. A., Brailovskaya V. A., Nikitin S. A., Polezhaev V. I., “Three-dimensional natural convection in a cubical enclosure: a benchmark numerical solution”, Proceedings of Int. Symp. on Advances in Computational Heat Transfer (Cesme, Izmir, Turkey, May 26–30, 1997), 157–165

[6] Leong W. H., Hollands K. G. T., Brunger A. P., “Experimental Nusselt numbers for a cubical-cavity benchmark problem in natural convection”, Int. J. Heat Mass Transfer, 42, 1979–1989 | DOI

[7] Fusegi T., Hyin J. M., Kuwahara K., “A numerical study of 3D natural convection in a differently heated cubical enclosure”, Int. J. Heat Mass Transfer, 34 (1991), 1543–1557 | DOI

[8] Artemev V. K., Rozhkov M. M., “Chislennoe modelirovanie trekhmernoi estestvennoi konvektsii v kubicheskoi polosti”, Fizicheskie osnovy eksperimentalnogo i matematicheskogo modelirovaniya protsessov gazodinamiki i teplomassobmena v energeticheskikh ustanovkakh, Trudy XIII Shkoly-seminara molodykh uchenykh i spetsialistov pod ruk. akad. RAN A. I. Leonteva (Sankt-Peterburg, 20–25 maya, 2001), 153–157