本文選題：線性化Navier-Stokes方程 + Crank-Nicolson有限差分法　； 參考：《昆明理工大學(xué)》2017年碩士論文

【摘要】：論文建立了線性化Navier-Stokes方程的Crank-Nicolson有限差分法,通過坐標(biāo)變換將不規(guī)則的物理區(qū)域映射到一個正方形計算區(qū)域,并在此計算區(qū)域設(shè)立交錯網(wǎng)格,反復(fù)耦合迭代,在此基礎(chǔ)上求解了該數(shù)學(xué)模型的數(shù)值解.文中主要數(shù)值模擬二維水槽內(nèi)自由面波高和渦場的變化規(guī)律,所做的主要工作和得到的結(jié)果有:(1)利用Crank-Nicolson有限差分法研究帶耗散線性化Navier-Stokes方程的數(shù)值解,并數(shù)值模擬自由振動和傾斜激勵晃動下自由面波高和渦場,數(shù)值結(jié)果表明,在自由振動中,自由面波高因粘性作用會發(fā)生衰減,且Reynolds數(shù)和耗散系數(shù)越大衰減越緩慢.在短時間性態(tài)傾斜激勵下,對于不同Reynolds數(shù)、耗散系數(shù)和傾斜激勵振幅會出現(xiàn)一定周期的單渦.(2)利用Crank-Nicolson有限差分法數(shù)值求解帶耗散線性化Navier-Stokes方程的解,并數(shù)值模擬傾斜激勵晃動和耦合的垂直和傾斜激勵晃動下的自由面波高和渦場.數(shù)值結(jié)果表明,經(jīng)過長時間性態(tài)的傾斜激勵,水槽內(nèi)渦場由單渦轉(zhuǎn)化成雙渦,而且在較高的Reynolds數(shù)和耗散系數(shù)條件下單渦出現(xiàn)周期更長.同時,在耦合的垂直和傾斜激勵下,自由面波高因粘性作用會發(fā)生衰減,且水槽內(nèi)流體在長時間性態(tài)作用下,雙渦只在傾斜激勵振幅較大條件下出現(xiàn).
[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.
【學(xué)位授予單位】：昆明理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O241.8

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