Chapter 0. Introduction to CFD and Computing
 Homework 1. Code Optimization (posted on Canvas)
Chapter 1. Foundamentals of Partial Differential Equation
Homework 2 (Posted in Canvas)
Chapter 2. Finite Difference Method
2.1. Introduction
2.2. Methods for Obtaining FD Expressions
Recording of Sept. 22.
5.1 Relexation Methods for Solving Elliptic Equations.
Term Project Part I
2.3. Quantitative Properties of FD Schemes.
Recording of Sept 27.
Homework 3
First Exam Review
Homework 4
Recording of Oct. 10.
2.4. MultiDimensional Problems
Chapter 3. Finite Difference Methods for Hyperbolic Equations
3.1. Introduction
3.2. Linear convection – 1D wave equation
Notes for 3.1 and 3.2
3.3. Phase and Amplitude Errors of
1D Advection Equation
Recording of Oct. 31.
Term Project Part II
Term Project All Parts
3.4. Monotonicity of Advection Schemes
3.5. MultiDimensional Advection
Recording of Nov. 2.
Recording of Nov. 7.
Previous lecture recording on practical measure of errors, monotonic schemes, multidimensional advection.
Previous lecture recording on multidimensional advection and nonlinear advection.
Homework 5
Second Exam Review
Chapter 4. Nonlinear Hyperbolic Problems
4.1. Introduction
4.2. Nonlinear Instability
4.3. Controlling Nonlinear Instability
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
4.5. Boundary Conditions for Hyperbolic
Equations
Chapter 5. Methods for Elliptic Equations
Chapter 6. Introduction to SemiLagrangian Methods
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 FiniteDifference Operators and Multigrid Solver. Monthly Weather Review, 141, 44504469.
 Heikes, R. and D. A. Randall, 1995: Numerical Integration of the ShallowWater Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of Tests. Monthly Weather Review, 123, 18621880.
 Heikes, R. and D. A. Randall, 1995: Numerical Integration of the ShallowWater Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy. Monthly Weather Review, 123, 18811887.
 GFDL CubicSphere Finite Volume (FV3, https://www.gfdl.noaa.gov/fv3/ ) model chosen as the new dynamic core of the National Weather Service nextgeneration global forecasting system (NGGPS), and potentially for the regional forecasting also.
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.
