AN EFFICIENT SCHEME FOR SOLVING STEADY INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

被引:134
作者
BRUNEAU, CH
JOURON, C
机构
[1] Université Paris-Sud, Laboratoire d'Analyse Numérique, 91405 Orsay
关键词
D O I
10.1016/0021-9991(90)90149-U
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The steady incompressible Navier-Stokes equations in a 2D driven cavity are solved in primitive variables by means of the multigrid method. The pressure and the components of the velocity are discretized on staggered grids, a block-implicit relaxation technique is used to achieve a good convergence and a simplified FMG-FAS algorithm is proposed. Special focus on the finite differences scheme used to approach the convection terms is made and a large discussion with other schemes is given. Results in a square driven cavity are obtained for Reynolds numbers as high as 15,000 on fine uniform meshes and the solution is in good agreement with other studies. For Re = 5000 the secondary vortices are very well represented showing the robustness of the method. For Reynolds numbers higher than 5000 the loss of stability for the steady solution is discussed. Moreover, some computations on a rectangular cavity of aspect ratio equal to two are presented. In addition the method is very efficient as far as CPU time is concerned; for instance, the solution for Re = 1000 on a 128 × 128 grid is obtained within 24 s on a SIEMENS VP 200. © 1990.
引用
收藏
页码:389 / 413
页数:25
相关论文
共 17 条
[1]  
Brandt A., 1979, NUMER METH PART D E, P53, DOI [10.1016/B978-0-12-546050-7.50008-3, DOI 10.1016/B978-0-12-546050-7.50008-3]
[2]  
CONSTANTIN P, 1985, MEM AM MATH SOC, V53, P314
[3]   A NUMERICAL-SIMULATION OF THE TRANSITION TO TURBULENCE IN A TWO-DIMENSIONAL FLOW [J].
FORTIN, A ;
FORTIN, M ;
GERVAIS, JJ .
JOURNAL OF COMPUTATIONAL PHYSICS, 1987, 70 (02) :295-310
[4]  
FORTIN M, 1971, J MECANIQUE, V10, P357
[5]   HIGH-RE SOLUTIONS FOR INCOMPRESSIBLE-FLOW USING THE NAVIER STOKES EQUATIONS AND A MULTIGRID METHOD [J].
GHIA, U ;
GHIA, KN ;
SHIN, CT .
JOURNAL OF COMPUTATIONAL PHYSICS, 1982, 48 (03) :387-411
[6]   MULTIGRID CALCULATION OF SUBVORTICES [J].
GUSTAFSON, K ;
LEBEN, R .
APPLIED MATHEMATICS AND COMPUTATION, 1986, 19 (1-4) :89-102
[7]   CAVITY FLOW DYNAMICS AT HIGHER REYNOLDS-NUMBER AND HIGHER ASPECT RATIO [J].
GUSTAFSON, K ;
HALASI, K .
JOURNAL OF COMPUTATIONAL PHYSICS, 1987, 70 (02) :271-283
[8]  
Hackbusch W., 1985, SPRINGER SERIES COMP, V4
[9]   COMPUTATION OF NATURAL-CONVECTION IN TWO-DIMENSIONAL CAVITIES WITH TSCHEBYSCHEFF POLYNOMIALS [J].
LEQUERE, P ;
DEROQUEFORT, TA .
JOURNAL OF COMPUTATIONAL PHYSICS, 1985, 57 (02) :210-228
[10]   VISCOUS AND RESISTIVE EDDIES NEAR A SHARP CORNER [J].
MOFFATT, HK .
JOURNAL OF FLUID MECHANICS, 1964, 18 (01) :1-18