I am trying to test the free surface simulation of a 2DV model with solitary wave. It gives me oscillations in the upstream side of the wave. Is there anyone who might know what the cause of the water surface oscillations could be? I guess it is something about implementing the initial and boundary conditions. I send the wave from left boudary by a time-dependent depth averaged velocity. Thanks

Is there any thing that prevent you from specifing the wave as an initial surface disturbance (one peak) profile ( I think it is a tanh function, see Wind wave book). You may assume zero velocities in the beginig or use a linear wave theory velocity distribution function. This should start the solution for a damping solitary wave.

The model simulates the initial disrturbance and small amplitude Stokes waves, but the solitary wave simultion is not satisfactory. I may not have completely understood the 2nd part of your comment, but a damped solitary wave would not match the analytical solution or did you mean somehting else? Thanks.

Are the oscillations unphysical?

If you look at the solution of the kdv equation then you will find that the soliton has an oscillatory tail. This is because the general solution is made up of solitons and cnoidal waves (the solitons are sech^2 profiles while the cnoidal waves are Jacobi elliptic functions -hence the cn).

Tom.

I mean use the analytical solution to initalize the variables fields just to start the solution.