METR 5344 CFD Course Home Page (Fall 2023)

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 5720

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

The following Zoom link will be used for office hours or remote access to class when neccessary:

We will use for assignment and grade posting.


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.
    • 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.

  • 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

  • Recording of Oct. 31.

  • Term Project Part II Term Project All Parts

    3.4. Monotonicity of Advection Schemes

    3.5. Multi-Dimensional Advection

  • 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

    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 Semi-Lagrangian Methods

    Chapter 7. Introduction to Spectral Methods

    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.