教學時程、課堂講稿
數值海洋流體力學
因舊版課程無指定課堂作業與考試，因此統整所有作業、講義、考試內容合併列出。
數值海洋流體力學
因舊版課程無指定課堂作業與考試，因此統整所有作業、講義、考試內容合併列出。
所有的課堂講稿能夠作為一份檔案下載 (PDF - 5.6 MB).
|
週 |
課程單元 |
課堂講稿 |
|
1 |
不可壓縮流體力學背景知識 Incompressible Fluid Mechanics Background (PDF) |
‧粒子圖像測速 Particle Image Velocimetry ‧平均化N－S方程 Averaged Navier-Stokes Equations ‧不可壓縮流體壓力方程 The Pressure Equation for an Incompressible Fluid ‧渦量方程 The Vorticity Equation ‧非粘性流體力學，Euler方程 Inviscid Fluid Mechanics, Euler's Equation ‧非粘性流體Bernoulli定理 Bernoulli Theorems for Inviscid Flow ‧渦量動力學與Kelvin環量定理 Vorticity Dynamics and Kelvin's Circulation Theorem ‧勢流與近似勢流 Potential Flows and Mostly Potential Flows ‧Green函數，Green定理與邊界積分方程 Green Functions, Green's Theorem and Boundary Integral Equations ‧求解範例 Example of Method Solution ‧從源和偶極子層角度理解邊界積分方程 Interpretation of Boundary Integral Equation in Terms of Source and Dipole Layers ‧Kelvin-Neumann問題 The Kelvin-Neumann Problem ‧Kelvin-Neumann的Green函數 The Kelvin-Neumann Green Function ‧源分佈與偶極子分佈 Source Only and Dipole Only Distributions ‧二維Green定理 Green's Theorem in Two Dimensions ‧渦力 Force on a Vortex ‧柱狀渦升力 Lift on a Vortex in a Cylinder ‧範例：用偶極子和渦設計二維機翼的平均線 Example: Design of 2D Airfoil Mean Line Using Dipoles and Vortices |
|
2 |
微積分中的有用結果Some Useful Results from Calculus (PDF) |
‧Gauss定理推導 Derivation of Gauss' Theorem ‧Gauss定理應用範例：船舶的 Froude Krylov振盪力 Example of Use of Gauss Theorem: Froude Krylov Surge Force on a Ship ‧運輸定理 The Transport Theorem ‧物體的壓力與力矩 Pressure Forces and Moments on an Object |
|
3 |
複數應用An Application Using Complex Numbers (PDF) |
‧複數編寫程式範例：圓到機翼的共形映射 Example of Programming with Complex Numbers: Conformal Mapping of a Circle into an Airfoil ‧壓力係數計算步驟 Procedure to Compute Pressure Coefficient |
|
4 |
方程求根Root Finding (PDF) |
‧二分法 Bisection Method ‧方程牛頓求根法 Newton's Method for Finding Roots of y(x) ‧矩陣代數回顧 Review of Matrix Algebra ‧矩陣行列式 Determinant of a Matrix ‧矩陣轉置與求逆 Transpose of a Matrix, Calculating the Inverse of a Matrix ‧矩陣範數 Matrix Norms ‧矩陣條件數 The Condition Number of a Matrix ‧高斯消元法 Gaussian Elimination ‧n維方程高斯消元的運算步數 Gaussian Elimination Operation Count for n Equations ‧線性方程數值求解的誤差，比例部分旋轉法則 Errors in Numerical Solutions of Sets of Linear Equations, Scaled Partial Pivoting Rule ‧LU分解法求解線性方程 Solution of Linear Equations by LU Decomposition ‧矩陣分解步驟 Procedure for Factorization of A |
|
5 |
曲線擬合與插值 Curve Fitting and Interpolation (PDF) |
‧函數的多項式逼近 Polynomial Approximation to a Function ‧拉格朗日多項式範例 Polynomials Example |
|
6 |
數值微分 Numerical Differentiation (PDF) |
‧有限差分法 Finite Difference Differentiation |
|
7 |
數值積分 Numerical Integration (PDF) |
‧梯行法 Trapezoidal Rule ‧梯行法的誤差 Trapezoidal Rule Error ‧一般梯行法 Usual Trapezoidal Rule ‧數值積分 Numerical Integration ‧Simpson法則 Simpson's Rule |
|
8 |
數值積分方程與數值微分方程 Numerical Integration of Differential Equations (PDF) |
‧Euler法，修正Euler法 Euler's Method, Modified Euler's Method ‧四階Runge－Kutta法 Fourth Order Runge Kutta Method ‧預估校正法 Predictor-Corrector Methods ‧高階微分方程 Higher Order Differential Equations ‧回顧與拓展 Review and Extension |
|
9 |
數值誤差範例Some Examples and Numerical Errors (PDF) |
‧數值流體動力學的類型，函數計算範例 Types of Numerical Hydrodynamics Problems, Example of Function Evaluation ‧常微分方程求解範例 Example of Solution of Ordinary Differential Equation ‧偏微分方程求解範例 Example of Solution of Partial Differential Equation ‧柱面座標 Cylindrical Coordinates ‧離散積分方程範例 Example of Discretized Integral Equation ‧穩定性 Stability |
|
10 |
板塊法 Panel Methods (PDF) |
‧擾動勢流邊界條件，三維流 Boundary Condition of Perturbation Potential, Three Dimensional Flows ‧深入理解Green定理 Interpretation of Green's Theorem ‧積分方程的排列 Arrangement of the Integral Equation ‧積分方程的數值形式 Numerical Form of the Integral Equation ‧生成數值方程 Making the Numerical Equations ‧求解步驟 Solution Steps ‧二維板塊法 Two Dimensional Panel Methods ‧二維積分方程的數值形式 Numerical Form of the Two Dimensional Integral Equation ‧產生升力的情況 Situations with the Generation of Lift ‧壓力與力的計算 Computation of Pressures and Forces |
|
11 |
邊界層 Boundary Layers (PDF - 1.3 MB) |
‧二維穩定邊界層方程 Two-Dimensional Steady Boundary Layer Equations ‧邊界層參數 Boundary Layer Parameters ‧品質通量 Mass Fluxes ‧邊界層動量積分求解範例 Example of Solution of Momentum Integral BL Equation ‧壓力分佈已知的湍流邊界層積分 Calculation of Turbulent Boundary Layer When Pressure Distribution is Known ‧層流封閉關係，湍流封閉關係 Laminar Closure Relations, Turbulent Closure Relations ‧海浪 Sea Waves ‧模擬範例 Example of Simulation ‧海洋光譜 Sea Spectra ‧傅立葉轉換 Fourier Transforms ‧實數的快速傅立葉轉換與反轉快速傅立葉轉換 Computational FFT and IFFT of Real Numbers ‧隨機波模擬 Simulation of Random Waves ‧傅立葉轉換、逆傅立葉轉換、快速傅立葉轉換與反轉快速傅立葉轉換與波模擬的回顧 Review of Fourier Transforms, Inverse Fourier Transforms, FFT's IFFT's and Wave Simulation ‧高斯亂數的產生（演算法經Everett F. Carter Jr允許使用） Generating Gaussian Random Numbers (Courtesy of Everett F. Carter Jr.) ‧波統計學 Wave Statistics ‧理論結果 Results from Theory ‧高斯隨機過程的定義 Definition of a Gaussian Random Process ‧1/n最高波平均波幅 Average Amplitude of the 1/n'th Highest Waves ‧極限波 Extreme Waves ‧剛性方程 Stiff Equations ‧水中水平淺吃水下垂纜線動力學 Dynamics of Horizontal Shallow Sag Cables in Water |
|
12 |
剛體振動Oscillating Rigid Objects (PDF) |
‧勢函數與邊界條件 Potentials and Boundary Conditions ‧細長體理論 Strip Theory ‧船體邊界條件 Boundary Conditions on Hull ‧搖擺，翻滾與偏航方程 Sway, Roll and Yaw Equations ‧船舶在隨機海況下運動模擬 Simulations of Ship Motions in Random Seas ‧附加阻力與漂流力 Added Resistance and Drift Forces ‧Gerritsma與Beukelman的附加阻力理論 Gerritsma and Beukelman Theory for Added Resistance ‧非線性波力計算 Nonlinear Wave Force Calculations ‧垂直海洋負載 Vertical Sea Loads |
附錄：板塊法與細長梯理論的進階資料（由Alexis Mantzaris提供）。Further Material on Panel Methods and Strip Theory (PDF - 1.0 MB)