An areal-averaged form of classical Shallow-Water-Equations is developed in conjunction with Finite-Volume-Method for capturing sub-grid bed variation. The averaging mechanism treats sub-grid obstacles through depth-dependent-area-averaged porosity at the macroscopic level. This porosity assumes a binary distribution (0,1) for a resolution fine enough to treat bed-variation separately, resulting in convergence of the developed framework to classical form. An attempt has been made to incorporate the unresolved fine-scale flow-information (e.g., micro-scale and cross-scale interaction components) in terms of the macroscopic variables through a non-linear closure model. An augmented approximated Riemann solver incorporates varying source–sink terms within interfacial fluxes along with discontinuous porosity and bed variation. The model is applied to three test-cases ranging from wave-interaction with trapezoidal porous block to dam-break flows through obstacle(s) with varying grid configurations. The coarse-scale formulation, along with closure, produces a reasonably accurate solution with minimal computational overhead.

中文翻译：

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通过面积平均浅水方程对城市洪水泛滥进行宏观建模


结合有限体积法开发了经典浅水方程的面积平均形式，用于捕获子网格床层变化。平均机制通过宏观层面上与深度相关的面积平均孔隙率来处理亚网格障碍物。该孔隙率假设二元分布 (0,1) 的分辨率足以单独处理床层变化，从而导致所开发的框架向经典形式收敛。人们尝试通过非线性闭合模型将未解决的精细尺度流动信息（例如，微观尺度和跨尺度相互作用分量）纳入宏观变量。增强近似黎曼求解器将界面通量中不同的源汇项以及不连续孔隙度和床层变化结合在一起。该模型应用于三个测试案例，从波与梯形多孔块的相互作用到溃坝水流通过具有不同网格配置的障碍物。粗尺度公式与闭包一起以最小的计算开销产生相当准确的解决方案。