Abstract The paper describes characteristics of numerical models of surface waves based on full equations for the flow with free surface in potential approximation, as well as their efficiency and applications. A more detailed description is given for the model using the surface following coordinate system. In such coordinate system Laplace equation for the potential transforms into a full elliptical equation that is solved as Poisson equations with iterations in the right-hand side. The method of solution based on separation into analytical solution and the deviation from it is offered. Such approach significantly accelerates the calculations. The problem on the whole is solved for the periodical in both horizontal directions Fourier domain using calculation of the nonlinear terms on a dense grid. The simulation of the wave field development under the action of wind and dissipation was carried out. It is demonstrated that transformation of the basic integral characteristics has a satisfactory agreement with the known data. All possible applications of the approach developed are described.

中文翻译：

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海浪的数值模拟

摘要 本文描述了基于势逼近自由表面流动的完整方程的面波数值模型的特点、效率和应用。使用表面跟随坐标系对模型进行了更详细的描述。在这样的坐标系中，势能的拉普拉斯方程转换为一个完整的椭圆方程，该方程作为泊松方程求解，在右手边进行迭代。提出了基于解析解的分离及其偏差的解法。这种方法显着加速了计算。使用密集网格上的非线性项计算，在两个水平方向的傅立叶域中从整体上解决了该问题。对风和耗散作用下的波场发展进行了模拟。结果表明，基本积分特性的变换与已知数据具有较好的一致性。描述了所开发方法的所有可能应用。