A robust prediction system should monitor all possible hydraulic transients, which is significant for the appropriate and safe operation of pipe systems. A second-order finite volume method (FVM) Godunov-type scheme (GTS) considering unsteady friction factors is introduced to simulate hydraulic transients, which was rarely involved in previous work. One explicit-solution source item approach developed in this work is crucial for the proposed GTS to easily incorporate various forms of the existing unsteady friction models, including original convolution-based models (Zielke model and Vardy–Brown model), simplified convolution-based model (Trikha–Vardy–Brown (TVB) model), and Brunone instantaneous acceleration-based model. Results achieved by the proposed models are compared with experimental data as well as predictions by the classic Method of Characteristics (MOC). Results show that the MOC scheme may produce severe numerical attenuation in the case of a low Courant number. The proposed second-order GTS unsteady friction models are accurate, efficient, and stable even for Courant numbers less than one and sparse grid, and only need much less grid number and computation time to reach the same numerical accuracy. The TVB convolution-based model and Brunone model in the second-order GTS are suggested for further applications in hydraulic transients due to their high accuracy and efficiency.

一个强大的预测系统应该监控所有可能的水力瞬变，这对于管道系统的适当和安全运行很重要。引入考虑非定常摩擦因素的二阶有限体积法 (FVM) Godunov 型方案 (GTS) 来模拟水力瞬态，这在以前的工作中很少涉及。在这项工作中开发的一种显式解决方案源项方法对于所提出的 GTS 很重要，它可以轻松地合并各种形式的现有非定常摩擦模型，包括原始的基于卷积的模型（Zielke 模型和 Vardy-Brown 模型），基于简化的卷积模型（Trikha-Vardy-Brown (TVB) 模型）和基于瞬时加速度的 Brunone 模型。将所提出的模型获得的结果与实验数据以及经典特征方法 (MOC) 的预测进行比较。结果表明，在低柯朗数的情况下，MOC方案可能会产生严重的数值衰减。所提出的二阶 GTS 非定常摩擦模型即使对于小于 1 的 Courant 数和稀疏网格也是准确、高效和稳定的，并且只需要更少的网格数和计算时间即可达到相同的数值精度。二阶 GTS 中的基于 TVB 卷积的模型和 Brunone 模型因其高精度和高效率而被推荐用于水力瞬态的进一步应用。所提出的二阶 GTS 非定常摩擦模型即使对于小于 1 的 Courant 数和稀疏网格也是准确、高效和稳定的，并且只需要更少的网格数和计算时间即可达到相同的数值精度。二阶 GTS 中的基于 TVB 卷积的模型和 Brunone 模型因其高精度和高效率而被推荐用于水力瞬态的进一步应用。所提出的二阶 GTS 非定常摩擦模型即使对于小于 1 的 Courant 数和稀疏网格也是准确、高效和稳定的，并且只需要更少的网格数和计算时间即可达到相同的数值精度。二阶 GTS 中的基于 TVB 卷积的模型和 Brunone 模型因其高精度和高效率而被推荐用于水力瞬态的进一步应用。