SPRING 2011 COURSE ANNOUNCEMENT
MATH 7740-01: Computational Incompressible Fluid Dynamics
Course Description
This is a one-time course intended to present a variety of numerical techniques and issues
related to the computation of incmpressible fluid flow in two and three dimensions. The course
will begin with a brief overview of the equations for fluid motion for velocity and pressure.
We will also use other formulations such as those based on vorticity and based on impulse.
The numerical methods expected to be discussed are some based on finite differences, projection
methods, and Lagrangian methods. We may discuss finite-element methods and finite volume methods
if time allows. Not all of these apply to every fluid motion. We will
discuss separately inviscid flows, Stokes flows, and more generally Navier-Stokes flows.
The issue of the appropriate boundary conditions for different formulations of the equations
will be a key component of the methods. We will address the accuracy and the order of convergence
of the methods.
Students will be expected to read journal articles and present material
Intended audience: Advanced undergraduates and graduate students
from mathematics, engineering and applied sciences.
Prerequisites: Basic numerical analysis, knowledge of a programming language.
Topics
Some of the topics covered are (not a comprehensive list):
- Quick review of the incompressible fluid equations
- Finite difference methods in velocity/pressure
- Projection methods
- Vorticity formulation and vortex methods
- Inviscid flows (Euler equations) and Lagrangian methods
- Stokes flows and regularization methods
Textbook
There will be no specific textbook but we will draw material from various sources.
Grades
The grade G will be computed based on homework and projects. The homework average will
count as one project and all project scores will count equally.
Exams
There will be no exams. Instead, there will be projects assigned during the semester.
Some projects will be in groups and some will be individual.
Homework
There will be occasional homework assignments.
Important dates
| Classes begin | Mon. Jan. 10 |
| MLK holiday | Mon. Jan. 17 |
| Mardi Gras break | Mar. 7-11 |
| Last day of class | Thu. Apr. 21 |
Sources
- Journals
- Books
- Online