复杂边界及实际地形上溃坝洪水流动过程模拟

Two-dimensional modelling of dam-break floods over actual terrain with complex geometries using a finite volume method

建立了基于无结构三角网格下采用有限体积法求解的二维水动力学模型,用于模拟溃坝洪水在复杂边界及实际地形上的流动过程。该模型采用Roe格式的近似Riemann解计算界面水流通量,结合空间方向的TVD-MUSCL格式及时间方向的预测-校正格式,可使模型在时空方向具有二阶计算精度。模型中引入最小水深概念,提出了有效的干湿界面处理方法。模拟了理想条件下溃坝水流过程,研究不同最小水深取值对干河床上洪水演进的影响,并用两组简单溃坝水流的水槽试验资料对模型进行验证。采用该模型模拟了实际溃坝洪水的流动过程,所得计算结果与实测资料及已有模型计算结果较为符合。

Based the total variation diminishing（TVD） finite volume method,a two-dimensional hydrodynamic model using unstructured triangular meshes is developed for modelling dam-break flooding under actual terrain with complex geometries.Details include uses of the Roe＇s approximate Riemann solver with the TVD-MUSCL（Monotone Upstream-centered Schemes for Conservation Laws） scheme as well as the procedure of predictor-corrector in time stepping,which can result in a second-order accurate solution for dam-break flows in both time and space.The moving boundary problem is resolved through the introduction of a minimum water depth concept that can efficiently treat the wetting and drying fronts during the model integration.The effect of using different values of the minimum water depth on the simulation of dam-break flows in the dry river bed is examined.We find that the minimum water depth can significantly alter the propagation of flood waves.Model results are also compared to the analytical solution under the idealized conditions,as well as two sets of dam-break data collected from flume experiments.Lastly,the model is validated using a real dam-break case with complex geometric conditions.The model simulation compares well with the observations and the other studies.