Numerical modeling of upstream propagation of a positive surge wave in an open-channel flow caused by a sudden rise of downstream water level, either by gate operation or by tidal influence, remains an important challenge from many aspects. A perusal of literature suggests that the Serre-Green-Naghdi (SGN) models have not been methodically explored for a positive surge flow modeling. In this study, the SGN equations for variable bed profiles are solved for simulating the positive surge waves. The governing equations are reformulated in the form of a conservation law, which is solved using a hybrid finite volume-finite difference method. The eddy-viscosity type wave breaking model is coupled with the governing equations for simulating a breaking surge. The performance of second- and fourth-order time stepping schemes and second- and fourth-order accurate schemes for determining the numerical flux is assessed. The results indicate that using an overall fourth-order accurate scheme is preferred for an accurate depiction of the positive surge waves. A comparison is also made with laboratory observations from a wide range of experiments conducted under different discharge, Froude number and bed slope conditions, which demonstrates that the proposed model can accurately reproduce the key free surface characteristics corresponding to positive surge waves. The importance of computing an accurate initial gradually varied flow profile before applying the transient downstream condition, such as a gate closure, is highlighted. Further, the significance of considering full non-linearity is demonstrated through numerical tests as the weakly non-linear Boussinesq-type equations are found to perform poorly in predicting the secondary undulations for an undular surge. The non-hydrostatic pressure field occurring during the propagation of an undular surge has rarely been reported from laboratory experiments. In this study, the bed pressure beneath a propagating undular surge is measured and compared with that computed according to the SGN equations. Finally, the results obtained from the proposed SGN model are compared with those obtained from Large Eddy Simulation results available in the literature.

从闸门操作或潮汐影响来看，由下游水位突然升高引起的，在明渠中正激波上游传播的数值模拟仍然是许多方面的重要挑战。大量文献研究表明，尚未针对正涌流模型系统地探索Serre-Green-Naghdi（SGN）模型。在这项研究中，求解了可变床剖面的SGN方程，以模拟正涌浪。控制方程以守恒律的形式重新制定，使用混合有限体积-有限差分法求解。涡粘性波浪破碎模型与控制方程相结合，用于模拟破碎浪涌。评估了用于确定数值通量的二阶和四阶时间步进方案以及二阶和四阶精确方案的性能。结果表明，最好使用整体的四阶精确方案来准确描述正浪涌波。还比较了在不同流量，弗洛德数和床坡度条件下进行的各种实验的实验室观察结果，这表明所提出的模型可以准确地再现与正浪涌相对应的关键自由表面特征。强调了在应用瞬态下游条件（例如闸门关闭）之前计算准确的初始逐渐变化的流量曲线的重要性。更多，通过数值测试证明了考虑完全非线性的重要性，因为发现弱非线性的Boussinesq型方程在预测波浪状波动的二次起伏方面表现不佳。实验室实验很少报道在波浪状浪涌的传播过程中出现的非静水压力场。在这项研究中，测量了传播的波浪状浪涌下的床层压力，并将其与根据SGN方程计算得出的床层压力进行了比较。最后，将从提议的SGN模型获得的结果与从文献中可获得的大涡模拟结果获得的结果进行比较。实验室实验很少报道在波浪状浪涌的传播过程中出现的非静水压力场。在这项研究中，测量了传播的波浪状浪涌下的床层压力，并将其与根据SGN方程计算得出的床层压力进行了比较。最后，将从提议的SGN模型获得的结果与从文献中可获得的大涡模拟结果获得的结果进行比较。实验室实验很少报道在波浪状浪涌的传播过程中出现的非静水压力场。在这项研究中，测量了传播的波浪状浪涌下的床层压力，并将其与根据SGN方程计算得出的床层压力进行了比较。最后，将从提议的SGN模型获得的结果与从文献中可获得的大涡模拟结果获得的结果进行比较。