基于Roe格式的不规则地形上浅水模拟  

Simulation of shallow water on irregular topographies based on approximate Riemann solver of Roe

作　　者：魏红艳[1,2] 梁艳洁 陈萌[5] 余明辉 WEI Hongyan;LIANG Yanjie;CHEN Meng;YU Minghui(State Key Laboratory of Water Resources and Hydropower Engineering Science. Wuhan University,Wuhan 430072,China;Department of Hydraulics,Yangtze River Scientific Research Institute,Wuhan 430010,China;Institute of Planning,Yellow River Engineering Consulting Co. ,Ltd.,Zhengzhou 450003,China;Postdoctoral Research Institute of Yellow River Engineering Consulting Co. ,Ltd. ,Zhengzhou 450003,China;Hubei Provincial Water Resources and Hydro power Planning,Survey and Design Institute,Wuhan 430064,China)

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,湖北武汉430072 [2]长江科学院水力学研究所,湖北武汉430010 [3]黄河勘测规划设计有限公司规划研究院,河南郑州450003 [4]黄河勘测规划设计有限公司博士后科研工作站,河南郑州450003 [5]湖北省水利水电规划勘测设计院,湖北武汉430064

出　　处：《武汉大学学报（工学版）》2019年第1期7-12,82,共7页Engineering Journal of Wuhan University

基　　金：国家自然科学基金资助项目(编号:11502174);中国博士后科学基金资助项目(编号:2016M592388);国家重点研发计划项目(编号:2016YFC0402604)

摘　　要：为准确求解不规则地形上的浅水方程,建立了一种基于Roe格式的黎曼近似解的具有二阶时间空间精度的和谐离散格式.守恒变量采用加入坡度限制的MUSCL(monotonic upstream-centred scheme for conservation laws)格式进行重构.为保证格式和谐性,引入水面梯度法并基于静水条件构造了底坡项的离散格式:河床梯度采用中心差分格式,而水深则为计算单元附近4个重构水深的平均值.将上述重新调整过的Roe-MUSCL格式运用于3个不规则地形上的水流算例,计算结果均比较理想.A well-balanced numerical scheme based on Roe’s approximate Riemann solver is established to solve the shallow water equations on irregular topographies.In the scheme,the predictor-corrector type finite volume scheme is used and the conservative variables are constructed with the MUSCL scheme(Monotonic Upstream-Centred Scheme for Conservation Laws).Thus the scheme is with second-order accuracy both in time and space.To establish the well-balanced scheme,the surface gradient method is introduced and a new discretization scheme of the bed slope source term has been constructed,in which the water depth is calculated by four reconstructed water depths.The well-balanced scheme has been tested by three examples of flow over irregular bed bottoms and satisfactory results have been acquired.

关 键 词：不规则地形 二阶精度 和谐格式 底坡源项 

分 类 号：TV145[水利工程—水力学及河流动力学]