Department of Aerospace and
Mechancial Engineering

AME 90936: Computational Fluid Mechanics

The course is intended for students that want to be able to solve the Navier Stokes and the Euler equations using finite volume and finite difference techniques. We start by a short introduction to where we solve the Navier-Sokes equation in a simple geometry using relatively simple approaches. Then we cover basic numerical concepts and solution methods for elliptic, parabolic and hyperbolic equations, ending by revisiting the Navier-Stokes equations. More advanced concepts such as high order advection and shock-capturing for hyperbolic systems, multigrid and Krylov methods for elliptic equations, adaptive grid refinement, imbedded boundary methods and interface tracking are then covered in some detail. We conclude by discussing emerging topics such as very large problems, multiscale and multiphysics problems, verification & validation and uncertainty quantification.

Background needed

This is a relatively advanced level treatment, but in all cases I will start a topic in a relatively elemantary way. The elementary aspects will, however, be covered quickly so students should have background in numerical methods and fluid dynamics. Some programming experience, such as with Matlab, is also essential.

Outline (tentative)

I have taught this course for a long time, in one form or another. However, new setting and a change in level has lead to some rearrangement of the material and the outline below is therefore likely to evolve as we proceed. For the tentative schedule, click on the link below:

Current Syllabus

Syllabus 2011

Syllabus 2010

Notice that in 2010 the course was taught at a more introductory level and that there were fewer lectures since the course was taught twice a week for an hour and a half each time. For the past three years I have recorded the lectures as I gave them (click on video) and I will attempt to do so again this year. Thus, you should be able go back if there is something you missed, or if you were unable to attend class.


Last updated 1/20/2013 by Gretar Tryggvason