Do you know a good and especially easy guide to code one's own Computational Fluid Dynamics solver, for the 2D Euler equations? I just would like to understand what commercial software like Fluent is doing. And when it's easy enough I would like to show some friends how to do and code that.

Unfortunately I couldn't find how to translate this http://en.wikipedia.org/wiki/Euler_equations_%28fluid_dynamics%29 into a numeric application.

Has anyone done this before? Any help is appreciated,

Andreas

Yes, lots of people have done it before.

The trick is to write conservation laws for mass, momentum, and energy as integral equations and turn them into matrix equations so you can solve them numerically. The transformation process usually involves discretizing a control volume using simple shapes like triangles and quadrilaterals for 2D and tetrahedra and bricks for 3D and assuming distributions of pertinent variables within the shape.

You'll need to know a fair amount about linear algebra, and numerical integration if the problem is transient.

There are several techniques for doing it: finite differences, finite elements, and boundary elements (if a suitable Green's function exists).

It's not trivial. You'll want to read something like this:

http://www.amazon.com/Numerical-Transfer-Hemisphere-Computational-Mechanics/dp/0891165223