水波传播的无网格数值模拟

在水波传播的数值模拟中采用了一种基于配点和径向基函数的无网格方法.采用Laplace方程的基本解作为径向基函数,将源点布置在模拟波浪场之外,沿边界布置配点而不是划分网格,从而自动满足控制方程,且不存在奇点,不需要求解积分方程.数值造波采用给定入射波面和速度势的方法,数值消波综合采用阻尼层消波和Sommerfeld辐射条件,非线性自由面的演化追踪采用二阶Taylor级数展开式.对线性规则波和非线性三阶Stokes波的模拟显示,数值结果与理论解吻合良好.表明无网格方法不但形式简单、计算速度快,而且稳定性和准确性令人满意,有望成为水波模拟问题的一种有效的数值方法.

The Numerical Simulation on Water Wave Propagation by Meshless Method

The meshless method was introduced to simulate the propagation of 2D water waves.Using the fundamental solution of the Laplace equation as the radial basis functions and locating the source points outside the computational domain,the problem of water wave propagation is solved by collocation of only a few boundary points.In order to improve the stability of numerical simulation,the incident wave elevation and velocity potential are applied to the wave generation.A sponge layer for wave damping absorber combined with the Sommerfeld radiation is used to the open boundary.The nonlinear free surface boundary conditions are used for determining the time stepping integration of wave elevation.The present model was applied to simulate the propagation of linear monochromatic waves and nonlinear Stokes waves.It is shown that the meshless method with no need of singular numerical integrations is easier to implement and computational time can be economized.Furthermore,good agreements are observed as compared with theoretical solution.