The paper describes the attempt to develop the accelerated method of simulation of 2-D surface waves with a use of 2-D model derived by simplifications of 3-D equations for potential periodic deep-water waves. The derivation is based on separation of velocity potential in surface-fitted coordinates into linear and non-linear components and analysis of exact Poisson equation for non-linear component of potential on a free surface. This equation contains both the first and second derivatives of velocity potential. The analysis of very accurate multiple solutions for velocity potential obtained with 3-D model shows that these variables are linearly connected to each other, what allows to obtain the 2-D equation for first derivative of potential (i.e., the vertical velocity on a surface), what gives the closed 2-D formulation for 3-D problem of 2-D waves. The connection between first and second variables is not precise; hence, the method as a whole cannot be exact. However, the 2-D model derived is able to reproduce different statistical characteristics of 2-D wave field with good accuracy. The most evident advantage of new model consists of absence of calculation of 3-D structure of velocity potential what increases a speed of calculations by about two orders.

本文描述了尝试使用2-D模型开发加速的2-D表面波模拟方法的尝试，该模型是通过简化潜在的周期性深水波的3-D方程式导出的。该推导是基于将表面拟合坐标中的速度电势分为线性和非线性分量，以及对自由表面上的电势的非线性分量进行精确的泊松方程分析。该方程式包含速度势的一阶和二阶导数。通过3-D模型获得的速度势的非常精确的多个解的分析表明，这些变量相互线性连接，这使得可以获得势的一​​阶导数（即，表面上的垂直速度）的2-D方程。 ），这为二维波的3-D问题提供了封闭的2-D公式。第一和第二变量之间的联系不精确；因此，该方法作为一个整体不能精确。但是，导出的二维模型能够以良好的精度再现二维波场的不同统计特性。新模型最明显的优势在于无需计算速度势的3-D结构，从而将计算速度提高了大约两个数量级。