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 (posted on Canvas)

Chapter 1. Foundamentals of Partial Differential Equation

• Letcure notes

• Chapter 1 from Lapidus & Pinder book
• D'Alember's Solution of wave equation.
• Recording of Sept. 12.
• Recording of Sept. 20.

Homework 2 (Posted in Canvas)

Chapter 2. Finite Difference Method

2.1. Introduction
2.2. Methods for Obtaining FD Expressions

Recording of Sept. 22.

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

5.1 Relexation Methods for Solving Elliptic Equations.

Term Project Part I

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

Recording of Sept 27.

Homework 3

First Exam Review

Homework 4

Recording of Oct. 10.

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) for schemes used in WRF ARW model.
• Janjic et al. (2001) for time integration scheme used in WRF NMM model.
• Takacs (MWR, 1985)
• Python Jupiter Notebook code for plotting amplification factor and phase error.

Recording of Oct. 31.

Term Project Part II Term Project All Parts

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)

Recording of Nov. 2.

Recording of Nov. 7.

Previous lecture recording on practical measure of errors, monotonic schemes, multi-dimensional advection.

Previous lecture recording on multi-dimensional advection and nonlinear advection.

Homework 5

Second Exam Review

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)

Recording of Nov. 9.

Recording of Nov. 13.

Previous lecture recording on control of nonlinear instability.

Previous lecture recording on control of nonlinear instability via conservation properties.

4.4 System of Hyperbolic Equations - Shallow Water Equation model

• Recording of Nov. 15.


• Mesinger and Arakawa (1976) Numerical methods used in atmospheric models. GARP Publication Series.
• Notes on controlling nonlinear instability
• Skamarock and Klemp (1992 MWR)


• Recording of Nov. 16.

4.5. Boundary Conditions for Hyperbolic Equations

• Klemp and Lilly (1978, JAS)


• Previous lecture recording on system of hyperbolic equations, Arakawa grids, boundary conditions.


• Recording of Nov. 28.

Chapter 5. Methods for Elliptic Equations

• Lecture Notes


• Fulton et al. MWR 1986 Multigrid review paper.


• Recording of Nov. 30.


• Previous lecture recording on boundary conditions, elliptic equations.

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


• Previous lecture recording on multi-grid method elliptic equations and semi-Lagrandian advection

Chapter 7. Introduction to Spectral Methods

• Lecture Notes


• Recording of Dec 5


• Previous lecture recording on spectral methods.


• 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.

Textbook (recommended but not required): 

Computational Fluid Mechanics and Heat Transfer, 4th Edition. Amazon Link.
Computational Fluid Mechanics and Heat Transfer, 3rd Edition. Amazon Link.