This study presents a method for determining the drag parameter in the 2D shallow water (SW) equation for flows through a coastal forest by conducting a series of 3D numerical simulations (3D NSs). Following the theory of multiscale modeling, an evaluation method procedure is proposed. We first prepare a local test domain that contains a sufficient number of trees to constitute part of a coastal forest. Then, 3D NSs are conducted in this test domain with various inflow conditions. Based on the corresponding results, the momentum losses over the test domain are converted into the drag parameter of the global SW equation. A response surface of the drag parameter is constructed as a function of the flow conditions. The stabilized finite element method is employed for both the local and the global NSs, and the phase-field method is utilized to represent 3D free surfaces. Comparisons between the 2D SW calculation results and the 3D NS results are also performed to verify the validity of the proposed method.

中文翻译：

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基于三维数值模拟的沿海森林浅水流阻力多尺度评价方法

本研究提出了一种通过进行一系列 3D 数值模拟 (3D NSs) 来确定流经沿海森林的 2D 浅水 (SW) 方程中阻力参数的方法。根据多尺度建模理论，提出了一种评估方法程序。我们首先准备一个本地测试域，其中包含足够数量的树木以构成沿海森林的一部分。然后，在具有各种流入条件的该测试域中进行 3D NSs。基于相应的结果，测试域上的动量损失被转换为全局 SW 方程的阻力参数。阻力参数的响应面被构造为流动条件的函数。局部和全局 NS 均采用稳定有限元方法，并且使用相场方法来表示 3D 自由表面。还进行了 2D SW 计算结果和 3D NS 结果之间的比较，以验证所提出方法的有效性。