Hi everyone,

What is the benefit of using explicit method in solving momentum equations in free surface flows, most of current softwares solve momentum equations explicitely and they have to use stability conditions in order to set time increment in the range that solution has stability. My question is that why noone (based on my knowledge) has used implicit method (for example SIMPLE algorithm or ...) to solve momentum equations which always is stable and there is no need to use any stability conditions!

I appreciate to receive your idea and comments about this matter.

Thanks Farhad

It's not just a question of stability. You need to ask (1) what time step do I require to resolve the surface gravity waves and (2) what is the effect of the timestepping procedure upon the phase speed and group velocity of the waves.

The solution using implicit methods may work for arbitrary large timesteps but that doesn't mean the solution is accurate. It's also possible that even when the timestepping is sufficiently small (this also goes for explicit methods) that the dispersion relation for the numerical waves may be adversely effected by the time discretization. There's some discussion of this, for the shallow water wave equations, in Wesseling's book "Principles of computational fluid dynamics".

"My question is that why noone (based on my knowledge) has used implicit method..."

Fluent has, and it has the drawbacks pointed out by Tom.

adding to previous comments,

when u need free surface flow with sharp interface, the stability of interface tracking method (such as VOF, Level set, MAC, ...) usually impose time step limitation (in fact CFL condition). so explict treatment of NS is sufficient.

Recently some time step free method for interface tracking were presented such as particle level set, CIP, ..., but their accuracy (physically correctness) is decreased with using large time step.

Thank you all for your helpful comments, I got the point right now.

Farhad