This paper presents a novel method of preserving well-balanced conditions for dam-break flows on irregular beds. The research on preservation of well-balanced conditions commonly deals only with spatial variation of beds. It is challenging to design a well-balanced scheme that can model both spatial and temporal variation of beds particularly on domains discretized with unstructured meshes. This challenge arises due to the non-trivial nature of the governing equations modeling hydro-morpho dynamics. This study proposes a new and simple well-balanced method applicable for both spatial and temporal bed variations without requiring additional treatment and complicated discretization of slope source terms. The work relies on a cell-centered Godunov-type finite volume method for solving coupled Saint Venant and sediment continuity equations. The two most important issues, i.e., the ‘lake at rest condition’ and ‘water depth positivity’ of shallow-water flows over irregular beds, are tested and verified in the proposed numerical scheme. The authors employed Riemann solvers to compute fluxes through the control volume surfaces. The proposed scheme is evaluated for various benchmark cases of dam-break flows on rigid and erodible beds. Comparisons between the results of the proposed numerical scheme, analytical solution, experimental data, and previous numerical observations show significant improvement for some cases and a good agreement in the rest.

本文提出了一种新颖的方法来保持不规则河床溃坝水流的均衡状态。关于保持平衡条件的研究通常只涉及床的空间变化。设计一个能够对床的空间和时间变化进行建模的均衡方案非常具有挑战性，尤其是在非结构化网格离散化的区域上。由于建模水动力形态动力学的控制方程具有非平凡的性质，因此出现了这一挑战。这项研究提出了一种适用于空间和时间床层变化的新的，简单的，均衡的方法，而无需进行额外的处理和对坡度源项进行复杂的离散化。这项工作依赖于以细胞为中心的Godunov型有限体积方法来求解圣维南和沉积物的连续性方程。在提出的数值方案中测试和验证了两个最重要的问题，即浅水在不规则河床上的“静止湖面”和“水深正值”。作者采用Riemann求解器来计算通过控制体积表面的通量。针对刚性和易蚀层上溃坝水流的各种基准案例，对所提议的方案进行了评估。所提出的数值方案，解析解，实验数据和先前的数值观测结果之间的比较表明，在某些情况下有显着改善，而在其他情况下则有很好的一致性。作者采用黎曼求解器来计算通过控制体积表面的通量。针对刚性和易蚀层上溃坝水流的各种基准案例，对所提议的方案进行了评估。拟议的数值方案，解析解，实验数据和先前的数值观测结果之间的比较表明，在某些情况下有显着改善，而在其他情况下则有很好的一致性。作者采用黎曼求解器来计算通过控制体积表面的通量。针对刚性和易蚀层上溃坝水流的各种基准案例，对所提议的方案进行了评估。拟议的数值方案，解析解，实验数据和先前的数值观测结果之间的比较表明，在某些情况下有显着改善，而在其他情况下则有很好的一致性。