Accurate and efficient numerical wave generation and absorption of two-dimensional nonlinear periodic waves traveling on a steady, uniform current were carried out in a potential, fully nonlinear numerical wave tank. The solver is based on the Βoundary Εlement Μethod (ΒΕΜ) with linear singularity distributions and plane elements and on the mixed Eulerian–Lagrangian formulation of the free surface equations. Wave generation is implemented along the inflow boundary by imposing the stream function wave solution, while wave absorption at both end-boundaries is effectively treated by introducing absorbing layers. On the absorbing beach side, the outflow boundary condition is modified to ensure that the solution accurately satisfies the dispersion relation of the generated waves. The modification involves a free-parameter that depends on the mass flux through the domain and is determined through a feedback error-correction loop. The developed method provides accurate time domain wave solutions for shallow, intermediate, and deep water depths of high wave steepness (wave heights up to 80% of the maximum value) that remain stable for 150 wave periods. This also holds in case a coplanar or opposing uniform current of velocity up to 20% of the wave celerity interacts with the wave.

中文翻译：

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在基于BEM的完全非线性数值波箱中以均匀电流传播的周期波的产生和吸收

在势能完全非线性的数值波箱中，进行了精确有效的数值波的产生和吸收，以稳定，均匀的电流传播的二维非线性周期波。求解器基于具有线性奇异性分布和平面元素的边界Element Method（ΒΕΜ），以及自由表面方程的混合欧拉-拉格朗日公式。通过施加流函数波解可沿流入边界实现波生成，而通过引入吸收层可有效处理两端边界处的波吸收。在吸收性海滩一侧，修改流出边界条件以确保解决方案准确地满足生成波的色散关系。修改涉及一个自由参数，该自由参数取决于通过域的质量通量，并通过反馈误差校正回路确定。所开发的方法为高陡度的浅水，中水和深水深度（波高高达最大值的80％）提供了稳定的时域波解决方案，这些深度在150个波周期内保持稳定。在高达20％的波速的共面或相反的均匀速度电流与波相互作用的情况下，也是如此。