Solitary wave


        As the results are not very good and there are some instabilities, the second part of this study is to improve the solution.

        Firstly, it is obvious that the instabilities grow very quickly and the wavelengh of them is very short. On the other hand the wavelengh of the solitary wave is very long. So a solution to reduce the instabilities is to reduce the number of cells. The mesh would be less precise and the cells would be bigger. The CFD code would not see the short wavelengh. In this case, the instabilities would disappear and the solitary wave would be always visible.

        So, after the alteration of the mesh, the results below are obtained :


To see the animation, put the mouse over the picture above.

        The instabilities still exist, but they are less signifiant. As we study big structures, it is not important to increase the size of the cells. So it is possible to reduce the influence of numerical instability.



        The alteration of the mesh improve the results, but there are still several problems.

        Indeed the instabilities appear particulary on the rear of the wave next to the corner. After some investigations we understand that there is a problem in the mesh. The cells before and after the corner are bigger than the others even if the angle is equal to 0 degree. For example :

        After some changes in the program which generates the mesh, this problem is solved.

        Others problems are corrected. For instance, the periodic boundary condition is corrected. Unfortunately there are still some problems.



        As the problems are important, we study the transformation of a solitary wave over an even bottom. We obtain the results below :


To see the animation, put the mouse over the picture above.

        With this animation, the celerity of the wave is determined. So : cexp = 3.29 m.s-1 and ctheo = 1,40 m.s-1.

        Moreover the growth of the wave is measured. So the wave is multiply by 0.06 per seconde.

        These results prove that there is a problem with the initial field. The picture below is another example.


To see the animation, put the mouse over the picture above.