Chapter 0. Introduction to CFD and Computing

• Syllabus

• Introduction to CFD

  • Narative

  • PowerPoint Presentation

  • Sample CFD Movies
    • ITSC Fluids Movie Archive
    • ARPS Simulation of a Supercell Storm (Mpeg movie)
    • 2D Density Current Movie One and Two using Java Script. More movies can be found at http://twister.ou.edu/density-current-2.html.
      
      
  • Reading Assignment: Chapter 1 of text bood Tannehill et al.
    
    

• Computers, Programming and Optimization

• Homework 1. Code Optimization.

Chapter 1. Basic Theories of PDE's

• Letcure notes Word Version

• Homework #2. PDE and Method of Characteristics
  

• Chapter 2. Finite Difference Method

  • 2.1. Introduction
    

  • 2.2. Methods for Obtaining FD Expressions
    

  • 2.3. Quantitative Properties of FD Schemes
    

  • 2.4. Multi-Dimensional Problems
    

• Chapter 3. Finite Difference Methods for Hyperbolic Equations
  

  • 3.1. Introduction

• 3.2. Linear convection - 1-D wave equation
  

• 3.3. Phase and Amplitude Errors of 1-D Advection Equation

  • Notes for sections 3.1-3
  • Durran (1991, MWR)
    
    

• 3.4. Monotonicity of Advection Schemes
  

• 3.5. Multi-Dimensional Advection

  • Smolarkiewicz (1982, MWR)
    
    
• Term project assignment
• ARPS mini Totorial
  
  

• Chapter 4. Nonlinear Hyperbolic Problems

• 4.1. Introduction
  
  
• 4.2. Nonlinear Instability
• 4.3. Controlling Nonlinear Instability
  • Xue (2001, MWR)
    
    
• 4.4 System of Hyperbolic Equations - Shallow Water Equation model
  
  
  • Review for second exam
    
    
• 4.5. Boundary Conditions for Hyperbolic Equations
  • Klemp and Lilly (1978, JAS)
    
    

• Chapter 5. Methods for Elliptic Equations
  

  • Fulton, Ciesielski and Schubert (MWR, 1985) - a review on multi-grid methods for solving elliptic equations
  • Skamarock, Smolarkiewicz and Klemp (1997, MWR) - An application of pre-conditional conjugate gradient method to solving elliptic equations.
    
    

• Chapter 6. Introduction to Semi-Lagrangian Methods

  • Staniforth and Cote (MWR, 1991) - a review on semi-Lagrangian method
    

• Chapter 7. Introduction to Spectral Methods
  

  • Review 3