Hello, I need help to solve Navier-Stokes Eq. using FEM-3D, to simulating of standing waves in a rectangular basin. Just a simple case. But I don,t know how it is. For Driven Cavity, it's easy. But there is "no free surface" in that case. Anybody could help me ? What kind of books I have to read, or papers, website etc. Thank you.

me, a student of Civil Eng. Gadjah Mada University -Yogyakarta, Indonesia

If you have a free surface with no prescribed velocity boundary condition, you may want to compute what the velocity should be on the free surface from the continuity eqn. Then update this boundary condition at every iteration until a converged solution results. Good luck. Chuck

Hi there,

As the name suggests, the free-surface is a boundary that is unknown and is part of the solution. Therefore, additional BC's must be added. This is the so-called double boundary conditions:

(1) dynamic BC: the traction at the free-surface must be balanced with the surface tension. This can be significantly simplified by ignoring the surface tension and viscous effect at the free surface.; (2) kinematic BC: the fact that no fluid particles leave the flow domain provides an additional BC.

Time marching is needed in an iterative manner, at least for the second BC. Another problem is the wave reflection if it is an infinite problem but solved in an finite domain. To my experience, wave damping technique is better.

Hope this helps.

Tony