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.