Hello
How can you say that the solution is damped. have you some measurements or a reference solution ?
The damping of the solution could be caused by several parameters. You have to look at the friction on the bed, the amount of diffusion you introduced, the order of the numerical scheme, the coarseness of the mesh etc...
Try, first, to explore the influence of theses parameters; you will undoubtedly immprove your solution.
with my best regards
Riadh