非线性波浪波面追踪的一种新模式

A new pursuit mode of nonlinear wave surface

基于Laplace方程的Green积分表达式和波面Bernoulli方程所建立的非线性波动数学模型,是一个时域上具有初始值的边值问题,而精确地追踪自由表面的波动位置,给出波面运动瞬时的波面高度和波面势函数,是建立时域内非线性波浪数值模式的基础。本文采用0 1混合型边界元剖分计算域边界并离散Laplace方程的Green积分表达式,采用有限元剖分自由水面并推导满足自由表面非线性边界条件的波面有限元方程,联立计算域内以节点波势函数和波面位置高度的时间增量为未知量的线性方程组,通过时步内的循环迭代,给出每个时步上的波面位置和波面势函数,从而建立了一种新的非线性波浪波面追踪模式。数值造波水槽内的波浪试验表明,其数值模拟结果具有良好的计算精度。

The numerical mode of nonlinear wave transformation based on both Laplace equation in water field and Bernoulli equation on water surface is a kind of time-domain boundary problem with initial conditions. And the basis of establishing the numerical mode of nonlinear wave in time domain is to trace the position of wave free surface and to calculate the instantaneous surface height and surface potential function. This paper first utilizes '0-1' combined BEM to separate the boundary with discretizing Green's integral equation based on Laplace equation, then separates the free surface of wave with FEM and derives FEM equation on wave surface that satisfies the nonlinear boundary conditions. By jointly solving the above BEM and FEM equations, the wave potential and surface height can be obtained with iteration in time domain. Thus a new kind of nonlinear numerical mode has been established for calculating wave transformation. The wave test in the numerical wave tank shows that the numerical simulation with this mode has very high accuracy.