A meshless numerical wave tank for simulation of fully nonlinear wave-wave and wave-current interactions

A meshless method is proposed to simulate fully nonlinear wave-wave and wave-current interactions in the time domain. The fully nonlinear free surface motion is simulated using the local radial point interpolation collocation method (LRPICM), material node approach, and fourth-order Runge-Kutta method (RK4). LRPICM is a truly meshless method and efficient for moving-boundary problems. Potential theory is used to describe the fluid flow, and the Laplace equation is solved in the Eulerian frame using LRPICM at each time step. The material node approach and RK4 are used to update the free surface boundary conditions. A regridding algorithm based on radial basis function interpolation is used to update the free surface moving boundary in a stable and accurate manner. The incident waves are imposed by feeding determined analytical waves on the input boundary. An efficient artificial damping zone is placed on the free surface before the downstream wall boundary to absorb wave energy and avoid any reflection of the waves. The numerical solutions are compared with experimental data, theoretical results, and other available numerical simulations.