Geodesic
Difference schemes on triangular and tetrahedral grids of Navier--Stokes equations for an incompressible fluid
Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 94-106.

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

The new approximations of Navier–Stokes equations for incompressible fluid on triangular and tetrahedral grids are proposed using predictor-corrector method. An estimations of unconditional stability of constructed schemes were fulfilled. The numerical solution of 2-D problem of flow field in a cavity with a mobile top cover was done (performed). The comparison with the other results was carried out. The questions of monotonisity of grid equations are discussed. 
@article{MM_2009_21_10_a9,
     author = {I. V. Popov and I. V. Fryazinov and M. Yu. Stanichenko and A. V. Taymanov},
     title = {Difference schemes on triangular and tetrahedral grids of {Navier--Stokes} equations for an incompressible fluid},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {94--106},
     publisher = {mathdoc},
     volume = {21},
     number = {10},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2009_21_10_a9/}
}
TY  - JOUR
AU  - I. V. Popov
AU  - I. V. Fryazinov
AU  - M. Yu. Stanichenko
AU  - A. V. Taymanov
TI  - Difference schemes on triangular and tetrahedral grids of Navier--Stokes equations for an incompressible fluid
JO  - Matematičeskoe modelirovanie
PY  - 2009
SP  - 94
EP  - 106
VL  - 21
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2009_21_10_a9/
LA  - ru
ID  - MM_2009_21_10_a9
ER  - 
%0 Journal Article
%A I. V. Popov
%A I. V. Fryazinov
%A M. Yu. Stanichenko
%A A. V. Taymanov
%T Difference schemes on triangular and tetrahedral grids of Navier--Stokes equations for an incompressible fluid
%J Matematičeskoe modelirovanie
%D 2009
%P 94-106
%V 21
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2009_21_10_a9/
%G ru
%F MM_2009_21_10_a9
I. V. Popov; I. V. Fryazinov; M. Yu. Stanichenko; A. V. Taymanov. Difference schemes on triangular and tetrahedral grids of Navier--Stokes equations for an incompressible fluid. Matematičeskoe modelirovanie, Tome 21 (2009) no. 10, pp. 94-106. http://geodesic.mathdoc.fr/item/MM_2009_21_10_a9/

[1] Belotserkovskii O. M., Chislennoe modelirovanie v mekhanike sploshnykh sred, Nauka, M., 1984, 520 pp. | MR

[2] Goncharov A. P., Devdariani M. T., Prostomolotov A. I., Fryazinov I. V., “Approksimatsiya i chislennyi metod resheniya trekhmernykh uravnenii Nave–Stoksa na ortogonalnykh setkakh”, Matematicheskoe modelirovanie, 3:5 (1991), 89–109 | MR

[3] Devdariani M. T., Prostomolotov A. I., Fryazinov I. V., “Finite difference method and program realization for solving three-dimensional Navier–Stokes equations in the cylinder”, Proc. of the IMACS International Conference on Mathematical Modelling and Applied Mathematics (Moscow, USSR, 18–23 June 1990), 119–132 | MR | Zbl

[4] Volkov P. K., Pereverzev A. V., “Metody konechnykh elementov dlya resheniya kraevykh zadach regulyarizovannykh uravnenii neszhimaemoi zhidkosti v peremennykh ‘skorost-davlenie’ ”, Matematicheskoe modelirovanie, 15:3 (2003), 15–28 | Zbl

[5] Eisenstat S. C., Sherman A. H., Subroutines for envelope solution of sparse linear systems, Research Rept, Dept. of Computation Science, Yale University, 1974, v. 112

[6] Kershaw D. S., “The incomplete Cholessky-Conjugate gradient method for the iterative solution of system of linear equation”, J. of Comput. Phys., 26 (1978), 43–65 | DOI | MR | Zbl

[7] Kershaw D. S., “On the problem of unstable pivots in the incomplete LU-Conjugate gradient method”, J. Comput. Phys., 38 (1980), 114–123 | DOI | MR | Zbl

[8] Popov I. V., Polyakov S. V., “Postroenie adaptivnykh neregulyarnykh treugolnykh setok dlya dvumernykh mnogosvyaznykh nevypuklykh oblastei”, Matematicheskoe modelirovanie, 14:6 (2002), 25–35 | MR | Zbl

[9] Popov I. V., “Novyi podkhod k postroeniyu tetraedralnoi setki”, Fundamentalnye fiziko-matematicheskie problemy i modelirovanie tekhniko-tekhnologicheskikh sistem, 10, 2007, 128–133

[10] Samarskii A. A., “O monotonnykh raznostnykh skhemakh dlya ellipticheskikh i parabolicheskikh uravnenii v sluchae nesamosopryazhennogo ellipticheskogo uravneniya”, Zh. Vychisl. Mat. i Matem. Fiz., 5:3 (1965), 548–550 | MR

[11] Golant E. I., “O sopryazhennykh semeistvakh raznostnykh skhem dlya uravnenii parabolicheskogo tipa s malymi chlenami”, Zh. Vychisl. Mat. i Matem. Fiz., 18:5 (1978), 1162–1169 | MR | Zbl

[12] Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matematicheskie zametki, 6:2 (1969), 237–248 | MR | Zbl

[13] Mazhorova O. S., Marchenko M. P., Fryazinov I. V., “Monotoniziruyuschie regulyarizatory i matrichnyi metod resheniya uravnenii Nave–Stoksa dlya neszhimaemoi zhidkosti”, Matematicheskoe modelirovanie, 6:12 (1994), 97–116 | MR | Zbl

[14] Ghia U., Chia K. N., Shin C. T., “High-Re Solutions for incompressible Flow Using the Navier–Stokes Equaton and a Multigrid Method”, J. of Computational Physics, 48 (1982), 387–411 | DOI | Zbl