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Numerical assessment of bed-load discharge formulations for transient flow in 1D and 2D situations

机译：一维和二维情况下瞬态流动的床荷排放配方的数值评估

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摘要

Two-dimensional (2D) transient flow over an erodible bed can be modelled using shallow-water equations and the Exner equation to describe the morphological evolution of the bed. Considering the fact that well-proven capacity formulae are based on one-dimensional (1D) experimental steady flows, the assessment of these empirical relations under unsteady 1D and 2D situations is important. In order to ensure the reliability of the numerical experimentation, the formulation has to be general enough to allow the use of different empirical laws. Moreover, the numerical scheme must handle correctly the coupling between the 2D shallow-water equations and the Exner equation under any condition. In this work, a finite-volume numerical scheme that includes these two main features will be exploited here in 1D and 2D laboratory test cases. The relative performances of Meyer-Peter and Muller, Ashida and Michiue, Engelund and Fredsoe, Fernandez Luque and Van Beek, Parker, Smart, Nielsen, Wong and Camenen and Larson formulations are analysed in terms of the root mean square error. A new discretization of the Smart formula is provided, leading to promising predictions of the erosion/deposition rates. The results arising from this work are useful to justify the use of an empirical sediment bed-load discharge formula among the ones studied, regardless of the hydrodynamic situation.
机译：可以使用浅水方程和Exner方程对可蚀层上的二维（2D）瞬态流动进行建模，以描述该层的形态演化。考虑到公认的容量公式基于一维（1D）实验稳定流这一事实，因此在不稳定的一维和二维情况下评估这些经验关系非常重要。为了确保数值实验的可靠性，该公式必须足够通用以允许使用不同的经验定律。而且，在任何条件下，数值方案都必须正确处理二维浅水方程和Exner方程之间的耦合。在这项工作中，将在1D和2D实验室测试用例中使用包含这两个主要特征的有限体积数值方案。根据均方根误差分析了Meyer-Peter和Muller，Ashida和Michiue，Engelund和Fredsoe，Fernandez Luque和Van Beek，Parker，Smart，Nielsen，Wong和Camenen和Larson公式的相对性能。提供了Smart公式的新离散化方法，从而可以预测腐蚀/沉积速率。不管流体动力情况如何，这项工作得出的结果对于证明在所研究的方法中使用经验性沉积物床荷排放公式是合理的。

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