# Inviscid fluid flow past a square cylinder.

1. Feb 19, 2012

### tarnhelm

The flow of an inviscid incompressible fluid around a circular cylinder is commonly studied in fluid dynamics courses. There's a wikipedia article about it here: http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder.

However, what about a square cylinder? There seem to be issues with simulating such flow across sharp edges or boundaries like the corners of squares. Can somebody tell me what you expect with such a scenario?

2. Feb 19, 2012

Actually a colleague of mine is about to publish a paper in the Journal of Fluid Mechanics on the viscous flow past a square cylinder. It is a very similar flow field to a circular cylinder but te vortex shedding is more complex. I'd say keep an eye on JFM for it, but it will probably be a year before it is actually published.

3. Feb 19, 2012

### tarnhelm

Thanks for that. I think there's a lot of stuff out there about viscous flow past a square cylinder. However, inviscid flow presents a problem because it may be the case that vortices are produced at the corners, which I don't think should be the case in inviscid flow. At the very least, finite difference simulations seem to produce this effect. As I understand it, steady incompressible inviscid flow shouldn't spontaneously develop rotation like this. I'm wondering if anybody has any more info about it, because google isn't turning up much!

4. Feb 19, 2012

### cjl

The problem is that a truly inviscid flow can turn around an arbitrarily sharp corner, which causes infinite acceleration of the fluid. This is clearly nonphysical. There isn't really a solution to this, which is why it is mostly ignored. If you decide to allow infinite acceleration, it would be qualitatively similar to the circular cylinder in terms of streamlines, but the corners would effectively be singularities in the flow. As for simulations, they have to have some inherent damping in order to converge, so they will never simulate truly inviscid flow.

Out of curiosity, why the interest in inviscid flow around corners? It's quite far from any physically realizable flow.

5. Feb 20, 2012

### zoobyshoe

A square cylinder? Someone will have to explain what that means to me.