Variational multiscale element free Galerkin method for the water wave problems

A new numerical method, which is based on the coupling between variational multiscale method and meshfree methods, is developed for the water wave problems, in which the free surface capturing technique is used to capture the position of the free surface. The proposed method takes full advantage of meshfree methods, therefore, no mesh generation and mesh reconstruction are involved. Meanwhile, due to that the proposed method belongs to meshfree methods, thus it is suitable for the highly deformed free surface flow problems. Finally, two water wave problems are solved and the results have also been analyzed. The numerical results show that the proposed method can indeed obtain accurate numerical results for the water wave problems, which does not refer to the choice of a proper stabilization parameter.