Geodesic
Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step
Matematičeskoe modelirovanie, Tome 28 (2016) no. 5, pp. 32-46.

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

The paper presents the results of numerical simulation of viscous incompressible fluid in a plane channel in an area of its sudden expansion. The calculations are based on a solving of system of two-dimensional Navier–Stokes equations in ‘velocity-pressure’ variables in the range of Reynolds numbers $100\leqslant\mathrm{Re}\leqslant 3000$. Particular attention is paid to the behavior of the solution near exit boundary through which, in general, takes place as the inflow and outflow of liquid from the domain. The algorithm for solving of the Neumann problem for pressure modification is described in detail, in which as a correction technique the difference analogue of the necessary condition of existence of solution is used. It is shown that the received fields of speed and pressure have minimum deviations in a narrow zone near the exit boundary even in case of short channels, which lengths aren't enough for display a full vortex behind the backward facing step.
Keywords: flow in a plane channel, Navier–Stokes equations
Mots-clés : mass balance. 
@article{MM_2016_28_5_a2,
     author = {A. A. Fomin and L. N. Fomina},
     title = {Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {32--46},
     publisher = {mathdoc},
     volume = {28},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_5_a2/}
}
TY  - JOUR
AU  - A. A. Fomin
AU  - L. N. Fomina
TI  - Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step
JO  - Matematičeskoe modelirovanie
PY  - 2016
SP  - 32
EP  - 46
VL  - 28
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2016_28_5_a2/
LA  - ru
ID  - MM_2016_28_5_a2
ER  - 
%0 Journal Article
%A A. A. Fomin
%A L. N. Fomina
%T Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step
%J Matematičeskoe modelirovanie
%D 2016
%P 32-46
%V 28
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2016_28_5_a2/
%G ru
%F MM_2016_28_5_a2
A. A. Fomin; L. N. Fomina. Numerical simulation of viscous incompressible fluid in a short plane channel with backward-facing step. Matematičeskoe modelirovanie, Tome 28 (2016) no. 5, pp. 32-46. http://geodesic.mathdoc.fr/item/MM_2016_28_5_a2/

[1] P. J. Roache, Computational fluid dynamics, Hermosa Publs., Albuquerque, 1976, 446 pp. | MR

[2] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, New York, 1980, 197 pp. | Zbl

[3] T. P. Chiang, T. W. H. Sheu, C. C. Fang, “Numerical investigation of vortical evolution in a backward-facing step expansion flow”, Applied Mathematical Modelling, 23 (1999), 915–932 | DOI | Zbl

[4] S. R. Batenko, V. I. Terekhov, “Vliianie dinamicheskoi predystorii potoka na aerodinamiku laminarnogo otryvnogo techeniia v kanale za obratnym priamougolnym ustupom”, Prikladnaia mekhanika i tekhnicheskaia fizika, 43:6 (2002), 84–92 | Zbl

[5] A. M. Bubenchikov, D. K. Firsov, M. A. Kotovshchikova, “Chislennoe reshenie ploskikh zadach dinamiki viazkoi zhidkosti metodom kontrolnykh obieemov na treugolnykh setkakh”, Matematicheskoe modelirovanie, 19:6 (2007), 71–85 | MR | Zbl

[6] E. V. Bruiatskii, A. G. Kostin, “Priamoe chislennoe modelirovanie techeniia v ploskom vnezapno rasshiriaiushchemsia kanale na osnove uravnenii Nave–Stoksa”, Prikladna gidromekhanika, 12:1 (2010), 11–27 | Zbl

[7] E. Erturk, “Numerical solutions of 2-D steady incompressible flow over a backward-facing step. Part I: High Reynolds number solutions”, Computers Fluids, 37 (2008), 633–655 | DOI | Zbl

[8] S. E. Rogers, D. Kwak, “An upwind differencing scheme for the incompressible Navier–Stokes equations”, Applied Numerical Mathematics, 8:1 (1991), 43–64 | DOI | MR | Zbl

[9] T. Lee, D. Mateescu, “Experimental and numerical investigation of 2-D backward-facing step flow”, Journal of Fluids and Structures, 12 (1998), 703–716 | DOI

[10] A. A. Mouza, M. N. Pantzali, S. V. Paras, J. Tihon, “Experimental Numerical study of backwardfacing step flow”, 5th National Chemical Engineering Conference (Thessaloniki, Greece, 2005)

[11] E. Erturk, “Discussions on driven cavity flow”, International Journal for Numerical Methods in Fluids, 60 (2009), 275–294 | DOI | MR | Zbl

[12] O. M. Belotserkovskii, V. A. Gushchin, V. V. Shchennikov, “Use of the splitting method to solve problems of the dynamics of a viscous incompressible fluid”, USSR Computational mathematics and mathematical physics, 15:1 (1975), 190–200 | DOI | MR | Zbl

[13] A. A. Fomin, L. N. Fomina, “Uskorenie polineinogo rekurrentnogo metoda v podprostranstvakh Krylova”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2011, no. 2(14), 45–54 | MR

[14] H. A. Van der Vorst, “Bi-CGStab: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems”, SIAM Journal on Scientific and Statistical Computing, 13:2 (1992), 631–644 | DOI | MR | Zbl

[15] A. A. Fomin, L. N. Fomina, “Chislennoe reshenie uravnenii Nave-Stoksa pri modelirovanii dvumernykh techenii viazkoi neszhimaemoi zhidkosti”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2014, no. 3(29), 94–108

[16] V. S. Vladimirov, V. V. Zharinov, Uravneniia matematicheskoi fiziki, Uchebnik dlia vuzov, Fizmatlit, M., 2004, 400 pp.

[17] B. F. Armaly, F. Durst, J. C. F. Pereira, B. Schonung, “Experimental and theoretical investigation of backward-facing step flow”, Journal of Fluid Mechanics, 127 (1983), 473–496 | DOI