CH EN 6355 – Computational Fluid Dynamics

Spring 2019 (Jan 7 – April 23, 2018)

Instructor: Prof. Tony Saad
Phone Number: 801 585 0344
Office Hours: Thursdays from 1:00 PM to 3:00 PM, by appointment, or if door is open
Office Location: MEB 2286

Course Catalog Description

Survey of approaches including time accurate and steady-state methods, explicit and implicit techniques. Eulerian and Lagrangian methods, laminar and turbulent flow, compressible and incompressible approaches, projection methods, stability considerations, etc. Application of CFD to mixing, heat transfer and reaction. Meets with CH EN 5353.
Cross listed with ME EN6720.

Course Objectives

Computational fluid dynamics has come to mean a variety of things depending on who you ask. At its core, however, CFD deals with calculation of a fluid flow. Whether the flow has chemical reactions, heat transfer, structures, etc… as long as there is fluid flow – you are doing CFD. Therefore it makes sense to focus on calculation of the fluid flow in a basic CFD course. We will cover and review the following concepts:

  • Review of transport theory, conservation laws, and the Navier-Stokes equations
  • Overview of advection/dispersion and diffusionHyperbolic Equations
  • Parabolic Equations
  • Elliptic equations
  • Putting it all together: the Navier-Stokes equations
  • Finite difference/finite volume methods
  • Verification and validation


You can find all Jupyter notebooks related to this course @ You can also view them cleanly at ttps://

Lecture # Topic Handouts Jupyter Notebooks Homework
Part I
1 Motivation
Harlow’s scientific memoir
NSF Fluid Mechanics films
IIHR Fluid Mechanics films
Anderson Chapter 1
2 The Navier-Stokes Equations – Part 1
videoslides (includes all parts)

Anderson Chapter 2
White Chapter 3
White Chapter 4
3 The Navier-Stokes Equations – Part 2
videoslides (see previous)
(see previous) HW1
4 Review of Finite Difference Methods (FDM)
Pletcher Chapter 3
Anderson Chapter 4
1D Advection FDM
5 Continuation of previous lecture
6 FDM for a Model Equation: Linear Advection Diffusion 
Error analysis, Stability, consistency, and convergence. 
Two-Dimensional Advection Equation
2D Advection FDM HW2
7 Solving the Navier-Stokes Equations using the Vorticity-Streamfunction Formulation
8 Continuation of previous lecture
2D Vorticity-Streamfunction Code
9 Solving the Navier-Stokes using Primitive Variables: The Projection Method (FDM)
Project 1
10 Continuation of previous lecture
2D Navier-Stokes Solver using the Finite Difference Method (lid-driven cavity example)
11 The Finite Volume Method
12 Finite Volume Navier Stokes on a Staggered Grid
13 Programming the Navier-Stokes FVM – Staggered Formulation
2D Navier-Stokes FVM Staggered
14 Project 1 presentations + intro to iterative solvers (see next lecture) HW 3
15 Iterative Solvers
video – no audio 🙁 – slides
Strang – Ch 7 Using sparse iterative solvers in Python Project 2
16 Guest Lecture: Parallel Computing for CFD (by Prof. James C. Sutherland)
video – slides
17 Numerical Phenomena (advection, diffusion, dispersion)
18 Hyperbolic Equations 1
video – slides
19 Hyperbolic Equations 2
video – slides (see previous)
Part II Core Algorithms and Analysis of Numerical Methods
Linear Solvers 1
Linear Solvers 2
Hyperbolic Equations 1
Hyperbolic Equations 2
Hyperbolic Equations 3
The Euler Equations 1
The Euler Equations 2
Revisiting the Advection-Diffusion Equation
Elliptic Equations 1
Elliptic Equations 2
Advanced NS Solvers
Other CFD Methods
Survey of commercial software
Part III Modeling & Complex Flows
Turbulent flows 1
Turbulent flows 2
Multiphase flows 1
Multiphase flows 2
Reacting flows 1
Reacting flows 2

Other Resources

You can find a collection of useful jupyter notebooks on Dr. Saad’s github repository:


This class will make exclusive use of Python – a modern programming language that is suitable for scientific computing. Python is easy to use and  – most importantly – free!

We will also focus on using Python within Jupyter Notebooks: a great way to combine text, math, and programming into one document that is edited and executed in a web browser (See this example). You will learn about that in the class. You will also have access to python through your web browser (after the class starts). If you want to download your own Python + Jupyter Notebook, then download the Anaconda distribution here.

Please go here for an easy tutorial on Python by Prof. Saad. In addition, Prof. Saad will hold a few in-class lectures on learning Python.

Python programming:

Python is very ubiquitous and a google search can usually turn up answers to many of your questions.  But here are a few ideas of places to look if you want to learn python:

Jupyter Notebooks:

Jupyter notebooks allow you to run Python code fragments interspersed with markup text including equations, plots, etc.  This is really useful for communicating results, and will be the format required for homework submission.

You will need to familiarize yourself with Jupyter notebooks since you will be submitting homework as a notebook.

Here is a link to a Jupyter notebook that provides a crash course on some of the key features of a notebook.

Web-Based Access for Jupyter Notebooks:

There are two options for web-based access to Jupyter

  1. You should have access to using your University login credentials for the duration of the semester.
  2. The chemical engineering virtual machine pool.  Log in with your ICC credentials and use the UG (not graduate) VM pools.  This will open a full windows machine where you can launch jupyter from the start menu.

These are great options if you have consistent web access and don’t want to perform a local python installation on your own laptop.


I will use your Email address to communicate with you and send information to class. Please make sure that you have access to your utah email address.


  • Homework is a fundamental piece of the learning process. It will help you strengthen the concepts you learned in class and apply them to new problems.
  • The goal of homework is to get you to familiarize yourself with the nomenclature and the types of problems that can be solved with numerical methods.
  • Homework assignments will be posted on the homework page of the course web site. Unless otherwise stated, homework is due by the beginning of class on the date indicated on the schedule.
  • Solutions will be posted on the class web site shortly after the due date.
  • Feel free to “work together” on homework assignments. Discuss the various solutions methods and attempt to learn or fill deficits in your understanding of the subject matter. However, you must submit your own original work. Please do not cross the line of plagiarism and cheating. Such behavior will not be tolerated.
  • Homework assignments must be submitted electronically via the course web page. You should write a report describing the problem, your solution, and presenting your results.

Grading policy (tentative)

  • 20% each midterm exam (two midterms)
  • 25% Homework
  • 10% In-Class comprehension quizzes
  • 25% Final exam

Grades will be assigned on the following scale, normalized to the highest student in the class (who, by definition, is 100%)

  • 92< A ≤ 100,   89 < A- ≤ 92
  • 86 < B+ ≤ 89,   81 < B ≤ 86,   78 < B- ≤ 81
  • 75 < C+ ≤ 78,   70 < C ≤ 75,   67 < C- ≤ 70
  • 64 < D+ ≤ 67,   59 < D ≤ 64,   56 < D- ≤ 59
  • E ≤ 56

I reserve the right to adjust this scale downward if I deem it necessary.

Addressing Sexual Misconduct

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Academic Misconduct

All instances of academic misconduct will be handled in accordance with the Student Code (

Students with Disabilities (ADA)

The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, (801) 581-5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.