METR 5344 CFD Course Home Page (Fall 2017)

Instructor: Dr. Ming Xue

mxue@ou.edu
NWC 2502 (CAPS Office Suite)
Tel: 325 6037
Personal Web Page: http://twister.ou.edu

Lecture Time: Tuesday, Thursday 1:00-2:15 pm
Location: NWC 5930

Office Hours: Tuesday and Thursday 11:00 - 12:30pm or by appointment
Location: NWC 2502

Chapter 0. Introduction to CFD and Computing

Chapter 1. Foundamentals of Partial Differential Equation

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.

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

3.4. Monotonicity of Advection Schemes

3.5. Multi-Dimensional Advection

Chapter 4. Nonlinear Hyperbolic Problems

4.1. Introduction
4.2. Nonlinear Instability

4.3. Controlling Nonlinear Instability

Review for second exam.

Homework 5.

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 Semi-Lagrangian Methods

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.

Review for third exam.