Meshless local Petrov-Galerkin method for two-dimensional nonlinear water wave problems

In this paper, the meshless local Petrov-Galerkin (MLPG) method is extended to dealing with nonlinear water wave problems. The formulation is based on general fluid governing equations and a time marching procedure. At each time step, the boundary value problem for the pressure is solved using the MLPG method; and the velocity and position of nodes are updated by numerical integration. The newly-extended method is applied to simulating water waves generated by a wave maker and good agreement with analytical solutions and finite element results is presented.