建立具有色散性的水平二维非线性波浪方程,方程的非线性近似到了三阶。方程以波面升高和自由表面速度势表达的微分-积分型数学方程,给出方程的数值求解方法和算例,对方程积分项的处理给出了计算方法。计算结果与Boussinesq方程模型和缓坡方程模型的对应计算结果进行了对比。
A horizontal 2D mathematical model with accurate dispersion for nonlinear water waves is presented. The nonlinearity of the equations is accurate to the third order in terms of wave steepness. The model is a set of differentiation-integral equations, and the cor- responding numerical solution method is recommended. Examples of numerical simulations are given and the results are compared with the results of the higher order Boussinesq equations and the mild slope equation.