Simulation of two-dimensional sloshing phenomenon by generalized finite difference method

Abstract

In this paper, a meshless numerical scheme, based on the generalized finite difference method (GFDM), is proposed to efficiently and accurately simulate the sloshing phenomenon in a two-dimensional numerical wave tank. When a numerical wave tank is excited horizontally or vertically, the disturbance on the free surface and the flow field in the tank is called sloshing. Based on the theorem of ideal fluid, the mathematical description of the sloshing problem is a time-dependent boundary value problem, governed by a second-order partial differential equation and two non-linear free-surface boundary conditions. In this paper, the GFDM and the explicit Euler method are adopted, respectively, for spatial and temporal discretizations of this moving-boundary problem. After the discretization by the explicit Euler method, the elevation of free surface is updated and a boundary value problem is yielded at every time step. Since the GFDM, a newly-developed domain-type meshless method, can truly get rid of time-consuming meshing generation and numerical quadrature, we adopted the GFDM to efficiently analyze this boundary value problem at every time step. To use the moving-least squares method of the GFDM can express the derivatives as linear combinations of nearby function values, such that the numerical procedures of the GFDM are very simple and efficient. We provided four numerical examples to verify the simplicity and the accuracy of the proposed meshless scheme. In addition, some factors of the proposed numerical scheme are systematically investigated via a series of numerical experiments.