摘要
本文对三维不可压缩N-S方程,采用了分层计算的新方法,即把层间的差分和层内的二维计算结合在一起,在层内采用有限分析法,对雷诺数为50、100、200和400,给出了三维及二维方腔流的计算结果。比较表明,方腔侧壁的存在,减小了主旋涡的强度,影响程度随雷诺数的加大而增强。文中同时也给出了三维方管层流的计算结果,与有关文献结果符合很好。
For the calculation of 3-D Navier-Stokes equations, the finite difference method and finite element method are commonly adopted to solve the primitive equations, Recently, C. J. Chen [1] calculated 3-D cavity flows in the finite analytic method of 3-D which demands to decide twenty-eight finite analytic coefficients of each local element so that the computation work is heavy. In order to dispose the correlation effect between velocities and pressure, the correction for the pressure is needed in the computation.In this paper, the stream vector and vorticity vector proposed in Ref[2,3,4] are employed to eliminate the pressure terms in the momentum equations to obtain the equations for the stream vector and vorticity vector. It's the default to get the pressure indirectly in this method. The separated layers method for the calculation is proposed by using the idea of Ref[5].to decrease the computation work. The main points of the separated layers method are that the computation domain is cutted in many layers along a determined coordinate in which three-dimensional governing equations are simplified to two-dimensional equations by putting the derivatives in the determined coordinate into the source terms and two-dimensional equations are solved by 2-D finite analytic method. The solution of 3-D Navier-Stokes equations is got through the iterations of approximate solutions among the layers.For Reynolds numbers are 50, 100, 200 and 400, the results of 3-D cavity flows are shown; for the purpose of comparisons, also results of 2-D cavity flows. The computation results of 3-D cavity flows indicate that the existance of side walls reduces the strength of the main vortexes, and its influence becomes stronger with increasing Reynolds numbers. The results of the viscous flow in 3-D square duct are given afterward, which are agreed well with that of Ref[4].
出处
《水动力学研究与进展（A辑）》
CSCD
北大核心
1989年第3期8-16,共9页
Chinese Journal of Hydrodynamics
