All of the lecture notes may be downloaded as a single file (PDF - 5.6 MB). Week 1: Incompressible Fluid Mechanics Background (PDF)
Particle Image Velocimetry
Averaged Navier-Stokes Equations
The Pressure Equation for an Incompressible Fluid
The Vorticity Equation
Inviscid Fluid Mechanics, Euler's Equation
Bernoulli Theorems for Inviscid Flow
Vorticity Dynamics and Kelvin's Circulation Theorem
Potential Flows and Mostly Potential Flows
Green Functions, Green's Theorem and Boundary Integral Equations
Example of Method Solution
Interpretation of Boundary Integral Equation in Terms of Source and Dipole Layers
The Kelvin-Neumann Problem
The Kelvin-Neumann Green Function
Source Only and Dipole Only Distributions
Green's Theorem in Two Dimensions
Force on a Vortex
Lift on a Vortex in a Cylinder
Example: Design of 2D Airfoil Mean Line Using Dipoles and Vortices
Week 2: Some Useful Results from Calculus (PDF)
Derivation of Gauss' Theorem
Example of Use of Gauss Theorem: Froude Krylov Surge Force on a Ship
The Transport Theorem
Pressure Forces and Moments on an Object
Week 3: An Application Using Complex Numbers (PDF)
Week 4: Root Finding (PDF)
Bisection Method
Newton's Method for Finding Roots of y(x)
Review of Matrix Algebra
Determinant of a Matrix
Transpose of a Matrix, Calculating the Inverse of a Matrix
Matrix Norms
The Condition Number of a Matrix
Gaussian Elimination
Gaussian Elimination Operation Count for n Equations
Errors in Numerical Solutions of Sets of Linear Equations, Scaled Partial Pivoting Rule
Solution of Linear Equations by LU Decomposition
Procedure for Factorization of A
Week 5:Curve Fitting and Interpolation (PDF)
Week 6: Numerical Differentiation (PDF)
Week 7: Numerical Integration (PDF)
Trapezoidal Rule
Trapezoidal Rule Error
Usual Trapezoidal Rule
Numerical Integration
Simpson's Rule
Week 8: Numerical Integration of Differential Equations (PDF)
Euler's Method, Modified Euler's Method
Fourth Order Runge Kutta Method
Predictor-Corrector Methods
Higher Order Differential Equations
Review and Extension
Week 9: Some Examples and Numerical Errors (PDF)
Types of Numerical Hydrodynamics Problems, Example of Function Evaluation
Example of Solution of Ordinary Differential Equation
Example of Solution of Partial Differential Equation
Cylindrical Coordinates
Example of Discretized Integral Equation
Stability
Week 10: Panel Methods (PDF)
Boundary Condition of Perturbation Potential, Three Dimensional Flows
Interpretation of Green's Theorem
Arrangement of the Integral Equation
Numerical Form of the Integral Equation
Making the Numerical Equations
Solution Steps
Two Dimensional Panel Methods
Numerical Form of the Two Dimensional Integral Equation
Situations with the Generation of Lift
Computation of Pressures and Forces
Week 11: Boundary Layers (PDF - 1.3 MB)
Two-Dimensional Steady Boundary Layer Equations
Boundary Layer Parameters
Mass Fluxes
Example of Solution of Momentum Integral BL Equation
Calculation of Turbulent Boundary Layer When Pressure Distribution is Known
Laminar Closure Relations, Turbulent Closure Relations
Sea Waves
Example of Simulation
Sea Spectra
Fourier Transforms
Computational FFT and IFFT of Real Numbers
Simulation of Random Waves
Review of Fourier Transforms, Inverse Fourier Transforms, FFT's IFFT's and Wave Simulation
Generating Gaussian Random Numbers (Courtesy of Everett F. Carter Jr.)
Wave Statistics
Results from Theory
Definition of a Gaussian Random Process
Average Amplitude of the 1/n'th Highest Waves
Extreme Waves
Stiff Equations
Dynamics of Horizontal Shallow Sag Cables in Water
Week 12: Oscillating Rigid Objects (PDF)
Potentials and Boundary Conditions
Strip Theory
Boundary Conditions on Hull
Sway, Roll and Yaw Equations
Simulations of Ship Motions in Random Seas
Added Resistance and Drift Forces
Gerritsma and Beukelman Theory for Added Resistance
Nonlinear Wave Force Calculations
Vertical Sea Loads
Appendix: Further Material on Panel Methods and Strip Theory (Courtesy of Alexis Mantzaris) (PDF - 1.0 MB)