# How to apply Navier-Stokes equations?

1. Sep 26, 2009

### Kricket

Hello all,

Still at my frisbee modeling program, I started to ask myself how I could get better approximations of stuff like COP versus angle-of-attack, drag/lift coefficients, etc. I've been checking out the Navier-Stokes equations because I understand they can be used to model fluid flow around an object? However, I'm having trouble seeing how I could write a simulator that would chug along and give me some useful values...

Can somebody give me an explanation of what would be required to apply these equations to a given object at a given velocity moving through the air? From what I can gather, it looks like solving the equations gives you the vector field for the air, which you would then use to calculate the force acting on the object at N different points on its surface...?

2. Sep 26, 2009

### xxChrisxx

Navier Stokes are a bunch of non-linear partial differential equations. They cannot be solves though convential means, unless the non-linear parts are = to zero. This means numerical techniques must be used, they arent plug and chug.

You would also never Solve NS equations directly as it would be computationally monsterous to try to calculate the exact movement of a fluid.

What is more commonly used is a time based approach. RANS (Reynolds averages Navier Stokes) uses turbulenc models and averaged flow to approximate a solution to NS.

Thta is basically all I can rememver from my fluids modelling course, someone else here who is better at maths will be able to explain in more detail.

3. Sep 26, 2009

### Kricket

Yeah, I know they're PDEs and a big pain in the poop-chute...I'm a computer/math guy and by "chug" I meant, write some complicated program that approximates a solution for a given tiny dt (and d-whatever else) a few thousand times, and see what comes out.

Alternatively, I've heard that there's (very expensive) professional software out there that does this; is there any chance of finding a demo version or perhaps a university that would let me use it for my small, simple example?

4. Sep 26, 2009

### thrillhouse86

Hey, a couple of things.

1. It may be overkill to solve your frisby problem with the Navier-Stokes equations - I mean I would start by looking at the Blaussius Approach to external viscous flow where you asymptotically patch together viscous solutions (with approximations) near your frisby with potential flow solutions far way from the frisby.

2. I'd be worried about creating a computer program, no matter how complicated for the standard Navier-Stokes equations because you'll find that your length scales become nightmarishly small.

3. Most Mechanical Engineering divisions will have CFD software, ACE is the one my university uses and it is quite easy to learn to use (although I wouldn't have a clue how to deal with a rotating object like a frisby). Although you'll find that unless the fluids academics are really good blokes your not going to be allowed to temporarily use their software - you'd do better to ask one of the students doing a fluids course for a cracked academic copy.

Regards,
Thrillhouse