Welcome!

This a teaching module for solving the Incompressible Navier-Stokes Equations computationally. The Navier-Stokes Equations govern the flow of an incompressible, viscous Newtonian fluid. We provide below a module (PDF or an online version) that teaches the basics of solving the equations computationally, using the now popular 'projection method' for discretising in time.

We provide a basic introduction to the Navier-Stokes Equations, and develop almost straight away a second-order finite difference method to solve the equations. The Python scripting language is used, in combination with C code in a Python C module, to demonstrate the ideas. Below we have a fully functional code which was used to create the figures on the right.

The Module

Click here to view the module online

Alternatively, you can download the module (PDF) which admittedly looks so much nicer than the online version!

Also available is the entire package: it includes

• PDF version of the module
• Python and C code
• README which contains instructions on how to use the code and what you need

Download the package (.zip file)

About

This module was created by Robert Saye, 2006.

A 3D surface plot of the x-component of the velocity field corresponding to a driven-lid cavity problem.

A vector field plot of a driven-lid cavity problem showing 3 nice vortices