基于非结构全混合网格的复杂地形二维水流数值模拟

Modeling of 2D shallow water flow in complex geometries based on unstructured hybrid meshes

为了进行复杂地形条件下的水流计算,该文以四边形网格为基础,对任意位置不满足变形控制条件的四边形网格加密为三角形网格来构建全混合的非结构网格,再采用有限体积法对浅水方程进行求解。模型利用混合流算例进行了静水、缓流以及混合流的计算;通过非平底溃坝水流算例对模型稳定性和处理地形干湿变化能力进行了验证,采用三角形网格计算用时为四边形网格的1.81,全混合网格则只有1.12。最后将检验后的模型对松花江哈尔滨主城区河段松浦退堤问题进行了模拟。结果表明:模型能较好模拟复杂地形条件下的水流运动,具有较高的计算效率和复杂边界适应性,可以为实际工程计算提供参考依据。

Unstructured triangular/quadrilateral hybrid meshes can be used to more easily simulate water flows in complex geometries.Hybrid meshes were generated using a quadrilateral mesh subdivision method with distortion control with a finite volume model based on the hybrid meshes used to simulate 2D shallow water flow.The model was validated with a classical trans-critical flow case.A dam-break was used to simulate flow over a wet／dry boundary to confirm its stability and robustness,where the computing time with a triangular mesh wad 1.81 times that of a quadrilateral mesh while at with a hybrid mesh was just 1.12 times.The model was then applied to flood control simulations influenced by the Songpu dike maintenance of the Harbin reach,Songhuajiang River.The results show that the model accurately simulates shallow water flows in complex topographies,is computationally efficient and flexible with irregular geometries,and provides valuable information for actual applications.