Chapter 0. Introduction to CFD and Computing

• Syllabus
  
  
• Introduction to CFD
  
  
  • Introduction - Presentation
  • Sample CFD Movies
    • CFD Gallery of Movies and Links to many more.
    • ARPS Simulation of a Supercell Storm (Mpeg movie)
    • ARPS Simulation of a Tornado (Mpeg movie) Movie (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.
    • Side by side comparison of radar observation and WRF forecast at 2 km horizontal grid spacing.
    • Side by side comparison of radar observation and WRF forecast at 1 km horizontal grid spacing.
  • 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.
  
• Homework 1. Code Optimization (assigned for 2020)

Chapter 1. Foundamentals of Partial Differential Equation

• Letcure notes

• D'Alember's Solution of wave equation.
• Chapter 1 from Lapidus & Pinder book
• Homework 2. (Assigned on September 24th)  
  

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

2.3. Quantitative Properties of FD Schemes.

• 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

Homework 3.

Review 1 for Exam 1

2.4. Multi-Dimensional Problems

Homework 4.

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) for schemes used in WRF ARW model.
• Janjic et al. (2001) for time integration scheme used in WRF NMM model.
• Takacs (MWR, 1985)

Homework 5, Part I.

3.4. Monotonicity of Advection Schemes

• Smolarkiewicz (1983, MWR)
• Zalasak (1979 JCP)
• ARPS tests with Robert (1993) test problem

3.5. Multi-Dimensional Advection

• Smolarkiewicz (1982, MWR)

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)

Review for second exam.

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
• Skamarock and Klemp (1992 MWR)

4.5. Boundary Conditions for Hyperbolic Equations

• Klemp and Lilly (1978, JAS)
• Homework 5 Part II

Chapter 5. Methods for Elliptic Equations

• Lecture Notes

Chapter 6. Introduction to Semi-Lagrangian Methods

• Lecture Notes
• Staniforth and Cote (MWR, 1991) - a review on semi-Lagrangian method
• Robert (1982) Paper on Semi-Lagarangian Semi-Implicit formulations

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
• ECMWF model information
  
  
• Model based on theicosaherdral grid:
• Heikes, R. P., D. A. Randall, and C. S. Konor, 2013: Optimized Icosahedral Grids: Performance of Finite-Difference Operators and Multigrid Solver. Monthly Weather Review, 141, 4450-4469.
  
• Heikes, R. and D. A. Randall, 1995: Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of Tests. Monthly Weather Review, 123, 1862-1880.
• Heikes, R. and D. A. Randall, 1995: Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy. Monthly Weather Review, 123, 1881-1887.
  
  
• GFDL Cubic-Sphere Finite Volume (FV3, https://www.gfdl.noaa.gov/fv3/ ) model chosen as the new dynamic core of the National Weather Service next-generation global forecasting system (NGGPS), and potentially for the regional forecasting also.

• Model for Prediction Across Scales–Atmosphere (MPAS-A) NCAR developed (https://mpas-dev.github.io/) :
• Skamarock, W. C., J. B. Klemp, M. G. Duda, L. D. Fowler, S.-H. Park, and T. D. Ringler, 2012: A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering. Monthly Weather Review, 140, 3090-3105.
  

Review for third exam.