二维不可压缩线性化Navier-Stokes方程流体动力学数值模拟研究

发布时间：2018-04-16 10:36

本文选题：线性化Navier-Stokes方程 + Crank-Nicolson有限差分法　；参考：《昆明理工大学》2017年硕士论文

【摘要】：论文建立了线性化Navier-Stokes方程的Crank-Nicolson有限差分法,通过坐标变换将不规则的物理区域映射到一个正方形计算区域,并在此计算区域设立交错网格,反复耦合迭代,在此基础上求解了该数学模型的数值解.文中主要数值模拟二维水槽内自由面波高和涡场的变化规律,所做的主要工作和得到的结果有:(1)利用Crank-Nicolson有限差分法研究带耗散线性化Navier-Stokes方程的数值解,并数值模拟自由振动和倾斜激励晃动下自由面波高和涡场,数值结果表明,在自由振动中,自由面波高因粘性作用会发生衰减,且Reynolds数和耗散系数越大衰减越缓慢.在短时间性态倾斜激励下,对于不同Reynolds数、耗散系数和倾斜激励振幅会出现一定周期的单涡.(2)利用Crank-Nicolson有限差分法数值求解带耗散线性化Navier-Stokes方程的解,并数值模拟倾斜激励晃动和耦合的垂直和倾斜激励晃动下的自由面波高和涡场.数值结果表明,经过长时间性态的倾斜激励,水槽内涡场由单涡转化成双涡,而且在较高的Reynolds数和耗散系数条件下单涡出现周期更长.同时,在耦合的垂直和倾斜激励下,自由面波高因粘性作用会发生衰减,且水槽内流体在长时间性态作用下,双涡只在倾斜激励振幅较大条件下出现.
[Abstract]:In this paper, the Crank-Nicolson finite difference method for linearized Navier-Stokes equation is established. The irregular physical region is mapped to a square computing area by coordinate transformation.On this basis, the numerical solution of the mathematical model is solved.In this paper, the variation of free surface wave height and vortex field in a two-dimensional flume is numerically simulated. The main work and results obtained are as follows: (1) the numerical solution of Navier-Stokes equation with dissipative linearization is studied by using Crank-Nicolson finite difference method.The free surface wave height and vortex field are numerically simulated under free vibration and inclined sloshing. The numerical results show that the free surface wave height attenuates due to viscosity in the free vibration, and the larger the Reynolds number and the dissipation coefficient, the slower the attenuation is.For different Reynolds numbers, the dissipation coefficient and the amplitude of tilting excitation will appear in a certain period of a single vortex under a short time tilted excitation. The Crank-Nicolson finite difference method is used to numerically solve the solution of the Navier-Stokes equation with dissipative linearization.The free surface wave height and vortex field under inclined and coupled vertical and inclined sloshing are numerically simulated.The numerical results show that the vortex field in the flume is transformed from a single vortex to a double vortex after a long period of inclined excitation, and the period is longer under the condition of higher Reynolds number and dissipation coefficient.At the same time, under the coupled vertical and inclined excitation, the free surface wave height will attenuate due to the viscous effect, and the double vortices will only appear under the condition of the larger amplitude of the inclined excitation under the action of the fluid in the flume for a long time.
【学位授予单位】：昆明理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O241.8

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