Hello,

I have a simple problem to solve : I try to model the flow of water on a non flat surface. The initial conditions would be a fixed height of water on the surface with initial velocity of zero. The surface is almost horizontal. With various type of boudary conditions. I don't need a software to do the job I wish to implement the solution. Indeed the flow solution is intended to be a part of a larger software. Another solution instead of programming could be interfacing to an existing solution. But then I face the following problem : the cost of the software. I can't imagine buying a complete cfd software just for that. Therefore in this case I would prefer a free solution I can integrate. Any advice ...

Thanks in advance

Regards

Christophe Absil

I can suggest an approach for you to consider. To do this, you have to be able to assume that the water is shallow relative to the 'horizontal' extents.

That is, if x & y are the directions over which the water is spread, then z measures the depth. And the maximum depth (z_max) is less than x_max and y_max which define the extent of the problem.

In that case most of the z-momentum equation and some of the terms in the x and y momentum equation go away. This is a boundary-layer type approach, so you might start with Schlichting. Also look at 'shallow water equations' in oceanography books or hydrology literature.

Basically you're exploiting the different scales of the horizontal and vetical motions to reduce the spatial dimensions from 3 to 2 and getting much simpler equations to solve in the bargain.

Depending on your level of physical intuition (or nerve!), further simplification might allow a closed form solution. The devil is in the details.

Hope this helps. Anything I've gotten wrong will be quickly corrected by following posters!