METR 5344 CFD Course Home Page (Fall 2015)

Instructor: Dr. Ming Xue
NWC 2502 (CAPS Office Suite)
Tel: 325 6037
Personal Web Page:

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

We will also use for grade posting etc.

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.

Review 1

Homework 3.

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

Homework 5.

Homework 5 Part II

Review 2.

Chapter 4. Nonlinear Hyperbolic Problems

4.1. Introduction
4.2. Nonlinear Instability

4.3. Controlling Nonlinear Instability

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

  • Model for Prediction Across Scales–Atmosphere (MPAS-A) NCAR developed recently:
  • 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.

  • A climate simulation model based on ICOSAherdraf 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.

  • An Icosahedral global model NOAA/ESRL is developing (FIM and subsequnet nonhydrostatic version):
  • Lee, J.-L. and A. E. MacDonald, 2009: A Finite-Volume Icosahedral Shallow-Water Model on a Local Coordinate. Monthly Weather Review, 137, 1422-1437.
  • Bleck, R., S. Benjamin, J. Lee, and A. E. MacDonald, 2009: On the Use of an Adaptive, Hybrid-Isentropic Vertical Coordinate in Global Atmospheric Modeling. Monthly Weather Review, 138, 2188-2210.

Review for 3rd Exam