内外模分离的三维浅水数学模型及通量格式研究  

Study on Three-dimensional Shallow Water Model with Inner-Outer Separated Modes and Its Flux Formulations

作　　者：宗思远 许栋 应超 及春宁[1] 冉启华 Zong Siyuan;Xu Dong;Ying Chao;Ji Chunning;Ran Qihua(State Key Laboratory of Hydraulic Engineering Simulation and Safety,Tianjin University,Tianjin 300072,China;Key Laboratory of Hydrologic-Cycle and Hydrodynamic-System of Ministry of Water Resources,Hohai University,Nanjing 210024,China;Zhejiang Institute of Hydraulics&Estuary(Zhejiang Institute of Marine Planning and Design),Hangzhou 310020,China)

机构地区：[1]天津大学水利工程仿真与安全国家重点实验室,天津300072 [2]河海大学水利部水循环与水动力系统重点实验室,南京210024 [3]浙江省水利河口研究院(浙江省海洋规划设计研究院),杭州310020

出　　处：《水动力学研究与进展（A辑）》2024年第5期756-766,共11页Chinese Journal of Hydrodynamics

基　　金：国家自然科学基金(52179076,51979186)。

摘　　要：该文建立了一种基于非结构化网格有限体积法的三维浅水流动模型。首先,通过联合求解内外模式的控制方程,利用外模式计算垂向积分方程以获取水位,再将其代入内模式求解三维浅水运动控制方程,得到流速的垂向分布,并应用k-ε紊流模型进行紊流封闭。水平方向上采用三角形网格,以获得更好的边界拟合效果;垂向方向上采用σ坐标系,以适应地形和水面起伏。为了优选精度高、计算速度快且易于编程实现的通量计算格式,该文对HLLC格式、Osher格式、FVS格式和Roe格式4种水平通量计算格式进行比较研究,并针对溃坝、干河床斜底溃坝和风生流过程进行了测试验证。结果表明,HLLC格式计算高效,能够很好地适应干湿变化且精度较高。最后,利用HLLC格式模拟经典航槽流动,进一步证实所建立的浅水模型具备模拟复杂三维分层流动的能力。In this paper,a 3-D shallow water model based on unstructured mesh finite volume method is established.By jointly solving the governing equations of the interior and exterior models,the vertical integral equation for water level is obtained using the exterior model.The water level is then used as an input to solve the three-dimensional shallow water motion control equations in the interior model,and the κ-ε model is applied for turbulent closure.A triangular mesh is used in the horizontal direction to achieve better boundary fitting,while a ρ coordinate system is adopted in the vertical direction to accommodate terrain and water surface fluctuations.In order to select a high-precision,computationally efficient,and easy-to-implement flux calculation scheme,a comparative study is conducted on four horizontal flux calculation schemes:HLLC,Osher,FVS,and Roe.The schemes are tested and validated for dam break,slant-bottom dam break,and wind-induced flow processes.The results show that theHLLC scheme is computationally efficient and suitable for dry-wet transition with relatively high accuracy.Finally,the HLLC scheme is used to simulate the flow in a navigation channel,further demonstrating the capability of the established shallow water model to simulate complex three-dimensional shallow water flows.

关 键 词：三维浅水方程 有限体积法 非结构网格 通量离散格式 

分 类 号：TE312[石油与天然气工程—油气田开发工程]