Generalized Finite Difference Method For Two Dimensional Free-surface Problems Of Water-wave

The research about wave transformation and free-surface propagation is great importance of coastal engineering.In this paper,the generalized finite difference method(GFDM),a meshless numerical method,is proposed to efficiently simulate two-dimensional free-surface problems of water-wave.The GFDM is a newly-developed domain-type meshless method which can truly get rid of time-consuming meshing generation and numerical quadrature,so it will improve the numerical efficiency at every time step.In addition,the numerical procedures of the GFDM are very simple because the partial derivatives can be expressed as linear combinations of nearby function values by the moving-least-squares method of the GFDM.Enforcing the satisfactions of governing equation at every interior node and boundary condition at every boundary node can acquire the extremely stable and accurate numerical solutions.Based on the theorem of ideal fluid,which is inviscid,irrotational and incompressible,three numerical models about wave by GFDM are proposed.Based on the Laplace equation in the wave field,two-dimensional free-surface sloshing problem in a numerical wave tank is discussed in the first numerical model.Based on the sloshing problem,the wave tank is extended into a long wave flume and shift the boundary conditions of tank to simulate the wave generation and propagation in the second topic.Lastly,the third numerical model is aim at two-dimensional horizontal free-surface problem,and we simulate a series of physical phenomenon about wave transformation and deformation based on the improved Boussinesq equations in 1996.In this paper,GFDM is applied in the series of numerical examples in a wave tank.Via the results from the proposed numerical scheme compared with numerical predictions and experimental observations from scholars in the past,it revealed the accuracy and applicability in the free-surface water-wave problems by the proposed numerical scheme.And it's clearly note that the numerical model is fully applied in the increased dispersive and more nonlinear wave field in the computational domain by some numerical examples in this research.Additionally,some factors of the proposed numerical scheme are also measured by a series of numerical experiments in order to demonstrate the stability and consistency of the proposed numerical scheme.