Normally sediments problems in rivers and channels can be solved by Navier–Stokes equations ..... It's depend on the values of flow velocity ..... You can see some simulations at Flow 3D website To understand the phenomena.Thanks
I am sorry Haitham but I have to differ on you on that point.I assume you mean sediment transport questions, but even then stating that these can be solved by the Navier-Stokes equations is a too big of a generalization.
Leaving the purely theorethical side apart and just focusing on the practical part of it there are some issues to consider:
- First of all it is the issue of the "transportability" or the "movebility" of the sediments. On that regard there is still a lot that is not fully understood and where the developed models (sediment transport equations) still fail by a factor of 2 (range between 50 - 200%) under simple geometry conditions, not to say in more complex geometries.
- 3D simulation requires such large amounts of computing capacity that either you need a super computer or you can only do it for a fairly small reach (and then you need to know your boundary conditions pretty well or you use a very coarse resolution. The last two approaches involve the introduction of errors and even the first one, relies on the not so well understood theories.
- There is the option of carrying out Direct Numerical Simulation, but that is still a growing field of research.