标题： 基于矩方法的耦合水文地貌沉积输运模型 显示英文标题

标题： A Coupled Hydro-Morphodynamic Model for Sediment Transport using the Moment Approach

摘要： 沉积物输运在浅水环境中自由表面流的水文地貌演化中至关重要，通常在浅水假设下对其进行建模。在经典的浅水沉积物输运模型中，流动的垂直结构被简化为深度平均和近床速度，通常通过经验方法重建，例如使用参数化的对数剖面。 实际上，这种经验剖面可能会有很大的变化。因此，在浅水框架内解决速度剖面的垂直结构以更好地逼近近床速度是至关重要的。本研究介绍了一种模型和模拟，该模型和模拟在沉积物输运中结合了垂直速度变化和底部侵蚀-沉积效应，为预测浅水环境中的沉积动力学提供了一个计算效率高的框架。我们采用所谓的矩模型方法来处理速度变化，这种方法考虑了水平速度在尺度化垂直方向上的多项式展开。 这允许使用一个复杂的速度剖面，该剖面由多项式基系数确定的一组扩展变量组成，从而在解决方案中解析垂直结构。扩展模型包括四个组成部分：（1）标准浅水方程；（2）控制基系数演化的矩方程；（3）沉积物浓度的演化方程；以及（4）底部的传输方程。这使得能够建立底载和悬浮载输运的耦合模型。我们使用双曲正则化技术确保模型的稳定性和现实的特征值。多个数值测试，包括有无湿/干前缘的溃坝情况，验证了我们的结果与实验室数据的一致性。 显示英文摘要

摘要： Sediment transport is crucial in the hydro-morphodynamic evolution of free surface flows in shallow water environments, which is typically modeled under the shallow water assumption. In classical shallow water modeling for sediment transport, the vertical structure of the flow is collapsed into a depth-averaged and near-bed velocity, usually reconstructed empirically, e.g., using a parameterized logarithmic profile. In practice, large variations from such empirical profiles can occur. It is therefore essential to resolve the vertical structure of the velocity profile within the shallow water framework to better approximate near-bed velocity. This study introduces a model and simulations that incorporate vertical velocity variations and bottom erosion-deposition effects in sediment transport, providing a computationally efficient framework for predicting sediment dynamics in shallow water environments. We employ the so-called moment model approach for the velocity variation, which considers a polynomial expansion of the horizontal velocity in the scaled vertical direction. This allows the use of a complex velocity profile with an extended set of variables determined by the polynomial basis coefficients, resolving the vertical structure as part of the solution. The extended model comprises four components: (1) the standard shallow water equations; (2) moment equations governing evolution of the basis coefficients; (3) an evolution equation for sediment concentration; and (4) a transport equation for the bed. This enables a coupled model for bedload and suspended load transport. We use a hyperbolic regularization technique to ensure model stability and realistic eigenvalues. Several numerical tests, including dam-break cases with and without wet/dry fronts, validate our results against laboratory data.