不可压缩Navier-Stokes方程数值模拟  

Numerical Simulation of Incompressible Navier-Stokes Equations

作　　者：胡丹丹 罗志强[1] HU Dan-dan;LUO Zhi-qiang(Department of Mathematics,School of Science,Kunming University of Science and Technology,Kunming 650500 China)

机构地区：[1]昆明理工大学理学院数学系,云南昆明650500

出　　处：《数学的实践与认识》2020年第14期188-199,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(11561037);云南省教育厅科学研究基金重点项目(2015z035)。

摘　　要：建立不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法,数值模拟了在初始正弦波下的二维水槽内流体受到倾斜激励时流场和涡的演变机制.数值结果表明,初始波为正弦波时,流场内出现一个单涡,单涡下沉变成了两个小涡,两个小涡消失后流场内部出现三条规则的流场带,最后这三条流场带演变成一个尖涡,尖涡在周围流体的作用下演变成一个单涡,最后单涡在自由面消失,当耗散系数和Reynolds数增大时,流场和涡演化的周期变小.A Crank-Nicolson finite difference method based on the incompressible NavierStokes equations is developed to numerically simulate the evolution of the flow field and vortex under the initial sine wave for pitching excitation.From the numerical results,we found that a single vortex exists in the tank with the initial sine wave in one peroid,and the single vortex descends into two small vortexes.Then the two vortexes disappear and flow fields break into three parts.After that,a tip vortex is developed and the vortex evolve into a single large vortex under the moving flow fluid.Finally,the single vortex disappear on the free surface.Especially when the dissipative parameter and Reynolds numbers increase,the period time of flow field and vortex decrease.

关 键 词：不可压缩NAVIER-STOKES方程 交错网格 Crank-Nicolson有限差分方法 涡 

分 类 号：O241.3[理学—计算数学]