摘 要
作為復(fù)雜的流體運(yùn)動(dòng)現(xiàn)象, 液體發(fā)生晃蕩時(shí)會(huì)伴隨產(chǎn)生波面破碎、波對(duì)艙壁的高速砰擊、液滴形成及氣泡卷入等強(qiáng)非線性現(xiàn)象，并表現(xiàn)出很強(qiáng)隨機(jī)性。本文對(duì)晃蕩現(xiàn)象數(shù)值研究現(xiàn)狀，特別是CIP法在晃蕩現(xiàn)象研究的發(fā)展進(jìn)行了較全面的回顧，在此基礎(chǔ)上，采用基于CIP(Constrained Interpolation Profile)法的自編程序，對(duì)晃蕩現(xiàn)象機(jī)理進(jìn)行研究。主要分為以下幾個(gè)內(nèi)容：
1) 系統(tǒng)介紹了CIP方法的基本原理以及應(yīng)用于晃蕩現(xiàn)象的處理。
詳細(xì)說(shuō)明了CIP方法與壓力修正(SIMPLE類)方法的區(qū)別與聯(lián)系，所采用的數(shù)學(xué)模型，利用CIP法對(duì)流場(chǎng)進(jìn)行分步求解的步驟。
2) 選定適當(dāng)?shù)臄?shù)值模型對(duì)晃蕩現(xiàn)象進(jìn)行描述并進(jìn)行程序的實(shí)現(xiàn)。
在原理介紹的基礎(chǔ)上實(shí)現(xiàn)程序編寫。結(jié)合CIP方法應(yīng)用于晃蕩現(xiàn)象的特點(diǎn)，采用交錯(cuò)網(wǎng)格描述流場(chǎng)信息，在邊界處采用虛網(wǎng)格保證邊界條件的處理。應(yīng)用帶有預(yù)處理矩陣K的Bi-CGSTAB方法求解壓力泊松方程，提高計(jì)算精度和效率。
3) 將所編制的程序用于潰壩問(wèn)題的模擬，以作為大變形自由液面的驗(yàn)算。
對(duì)潰壩過(guò)程中的液面變化進(jìn)行了監(jiān)測(cè)，與Fluent計(jì)算結(jié)果相比較，驗(yàn)證所編寫程序可以對(duì)自由液面進(jìn)行很好的捕捉；對(duì)潰流下游固定壁面處壓力測(cè)點(diǎn)的載荷變化進(jìn)行監(jiān)測(cè)，與實(shí)驗(yàn)結(jié)果的比較表明，所編寫程序可以反映流場(chǎng)中壓力的變化。
4) 在潰壩模擬驗(yàn)算的基礎(chǔ)上，利用自編程序進(jìn)行晃蕩問(wèn)題的研究。
針對(duì)不同液深及晃蕩幅值的工況進(jìn)行相應(yīng)計(jì)算，在非諧振激勵(lì)下，各種液深下的晃蕩強(qiáng)度均小于諧振激勵(lì)，但高液深時(shí)的差異較小。對(duì)壁面壓力進(jìn)行監(jiān)測(cè)發(fā)現(xiàn)，當(dāng)艙內(nèi)形成駐波，艙壁所蔃@寤餮沽ο災(zāi)湫　�

關(guān)鍵詞：CIP；液體晃蕩；Bi-CGSTAB；自由液面；潰壩



Abstract
Violent sloshing is a strongly nonlinear problem, which may involve phenomena such as breaking waves, high-speed impacts on tank walls, liquid droplet formation and air bubble entrainment, and is of high randomness. In this paper, the state of the art of the study on sloshing with numerical method, especially the application of the CIP method in sloshing simulation is reviewed. Some research about the mechanism of sloshing has been taken based on the foundation, with the self-programming code of Fortran language. The main work and important conclusions of this paper are listed as follows:
1) Give an overall review of the principle of CIP method and the application is sloshing
Specify the difference between fractional step method and pressure correction method, choose proper mathematic model to describe the sloshing phenomenon, and describe the fractional solving steps with CIP method.
2) The choice of proper numerical model and programming
Program with Fortran language based on the introduction. Combining the characteristics of the CIP method applied to sloshing phenomenon, staggered grid is adopted to store the information of the fluid field, and an exterior fictitious one-cell layer adjacent to each side of the physical domain is added to allow imposition of discrete boundary condition. Use the Bi-CGSTAB method with preconditioning matrix K to calculate the Poisson equation of pressure precisely and efficiently.
3) Simulate the dam-breaking problem to validate the code in the use of large deformation of free surface
Monitor the deformation of the free surface, and compare the result with computation by Fluent, which certify the capture of the free surface; the comparison between the monitored pressure and experimental data at the solid wall downstream showed that the code is feasible to monitor the variant of the pressure.
4) Simulate the sloshing phenomenon with the code based on the validation of the dam-breaking problem
Cases of different liquid level and sloshing amplitude are simulated. The results show that the intensity of sloshing in the bestir of the non-resonance frequency is smaller than the resonance frequency liquid with both depths, while in high level cases the difference is not obvious; the monitored pressure show that the slamming pressure is much smaller when stationary waves are formed in the tank.
Key word: CIP method; liquid sloshing; Bi-CGSTAB method; free surface; dam breaking


目 錄
摘 要 I
Abstract III
第1章 緒論 1
1.1 選題的背景和意義 1
1.2 本課題的國(guó)內(nèi)外研究現(xiàn)狀與發(fā)展趨勢(shì) 1
1.2.1 晃蕩數(shù)值研究簡(jiǎn)介 1
1.2.2 CIP法簡(jiǎn)介及其在晃蕩研究中的相關(guān)應(yīng)用 3
1.3 本文的工作 8
第2章 CIP法的基本原理 9
2.1 引言 9
2.2 半拉格朗日(Semi-Lagrange)格式 10
2.3 CIP法 11
2.3.1 一維CIP算法 11
2.3.2 二維CIP算法 12
2.4 分步算法思想 15
2.5 交錯(cuò)網(wǎng)格及變量存儲(chǔ)規(guī)則 17
2.6 本章小結(jié) 18
第3章 基于CIP法的自由液面流場(chǎng)數(shù)值求解 19
3.1 控制方程 19
3.2 基于CIP方法的流場(chǎng)分步求解過(guò)程 21
3.3 確定自由液面——密度函數(shù)的計(jì)算 24
3.4 笛卡爾網(wǎng)格法 26
3.5 壓力Poisson方程的迭代求解 27
3.6 帶有預(yù)處理矩陣的Bi-CGSTAB算法 30
3.7 本章小結(jié) 30
第4章 晃蕩模型的建立與數(shù)值離散 31
4.1 基本假定 31
4.2 控制方程 31
4.3 外界激勵(lì)的加載與參考系的選取 32
4.4 定解條件 32
4.4.1 初始條件 32
4.4.2 邊界條件 34
4.5 程序設(shè)計(jì) 35
4.5.1 程序功能模塊與結(jié)構(gòu) 35
4.5.2 程序?qū)崿F(xiàn)流程 37
4.6 本章小結(jié) 38
第5章 應(yīng)用于潰壩問(wèn)題的計(jì)算 39
5.1 自由液面微幅變形的計(jì)算 39
5.1.1 模型的選取與建立 39
5.1.2 計(jì)算結(jié)果分析 40
5.2 自由液面的大幅變形&..