Abstract Averaging techniques are used to generate upscaled forms of the shallow water equations for storm surge including subgrid corrections. These systems are structurally similar to the standard shallow water equations but have additional terms related to integral properties of the fine-scale bathymetry, topography, and flow. As the system only operates with coarse-scale variables (such as averaged fluid velocity) relating to flow, these fine-scale integrals require closures to relate them to the coarsened variables. Closures with different levels of complexity are identified and tested for accuracy against high resolution solutions of the standard shallow water equations. Results show that, for coarse grids in complex geometries, inclusion of subgrid closure terms greatly improves model accuracy when compared to standard solutions, and will thereby enable new classes of storm surge models.

中文翻译：

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风暴潮建模的子网格理论

摘要 平均技术用于生成包括子网格校正在内的风暴潮浅水方程的放大形式。这些系统在结构上类似于标准浅水方程，但具有与精细水深测量、地形和流动的整体属性相关的附加项。由于系统仅使用与流量相关的粗尺度变量（例如平均流体速度）运行，因此这些细尺度积分需要闭包以将它们与粗化变量相关联。针对标准浅水方程的高分辨率解，识别和测试具有不同复杂程度的闭包的准确性。结果表明，对于复杂几何中的粗网格，与标准解相比，包含子网格闭合项大大提高了模型精度，