Chapter 0. Introduction to CFD and Computing

• Syllabus
  
  
• Introduction to CFD
  
  • Narative
  • PowerPoint Presentation
  • Sample CFD Movies
    • CFD Gallery of Movies
    • ARPS Simulation of a Supercell Storm (Mpeg movie)
    • ARPS Simulation of a Tornado (Mpeg movie) Movie 1 and Movie 2 (permission from Ming Xue needed to use the movies).
    • 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 book
    
    
• Computers, Programming and Optimization
  • Assignment - Go through presentation An Introduction to High-Performance Computing by Henry Neeman or a Local Copy of the same presentation
    
    
• Another Presentation by Henry Neeman on compiler optimization will also very be helpful.
  
  
• OSCER Topdawg Quick Guide
  
  
• Homework 1. Code Optimization. hw1.f90 Example Answer

Chapter 1. Foundamentals of Partial Differential Equation

• Letcure notes

• D'Alember's Solution of wave equation.
• Chapter 1 from Lapidus & Pinder book

Homework 2.

Chapter 2. Finite Difference Method

2.1. Introduction
2.2. Methods for Obtaining FD Expressions

Tremback et al (1987 MWR) - an example of using interpolation and polynomial fitting to construct high-order advection scheme

Homework 3.

2.3. Quantitative Properties of FD Schemes. Lecture notes

Durran Chapter 2 on Finite Different Methods

Straka et al (1993) on numerical convergence and determination of order of accuracy

Fletcher book sections on solving diffusion equations

Pielke book section on stability of schemes for diffusion equations

Handouts on solving tridiagonal system of equations

Fletcher book sections on general concepts and numerical convergence

Exam 1 Review Guide | Grade distribution

Homework 4.

2.4. Multi-Dimensional Problems

Chapter 3. Finite Difference Methods for Hyperbolic Equations

3.1. Introduction
3.2. Linear convection – 1-D wave equation

Notes for 3.1 and 3.2

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

• Durran (MWR 1991). Also read sections in Durran Chapter 2 linked to earlier.
• Wicker and Skamarock (MWR 1998, 2002).
• Takacs (MWR, 1985)

3.4. Monotonicity of Advection Schemes

• Smolarkiewicz (1983, MWR)

3.5. Multi-Dimensional Advection

• Smolarkiewicz (1982, MWR)

Homework 5 .

Exam 2 Review Guide | Grade distribution

Chapter 4. Nonlinear Hyperbolic Problems

4.1. Introduction
4.2. Nonlinear Instability

• Notes for 4.1-4.3.
• Philips (1959)

4.3. Controlling Nonlinear Instability

• Xue (2000, MWR)

4.4 System of Hyperbolic Equations - Shallow Water Equation model

• Mesinger and Arakawa (1976) Numerical methods used in atmospheric models. GARP Publication Series.
• Notes on controlling nonlinear instability

4.5. Boundary Conditions for Hyperbolic Equations

• Klemp and Lilly (1978, JAS)

Homework 6

Chapter 5. Methods for Elliptic Equations

• Lecture Notes
• 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

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

Chapter 7. Introduction to Spectral Methods

• Lecture Notes
• Durran book Chapter 4
• Temperton (2000) on future of spectral method for ECMWF model
• Cullen et al (2000) on key issuess for future development of ECMWF model

Study Guide for 3rd Exam