基于非结构混合网格求解二维浅水方程的一种数值方法  

A total variation diminishing scheme for two-dimensional shallow water equations on mixed unstructured grids

作　　者：董炳江 卢新华[2] 袁晶 

机构地区：[1]长江水利委员会水文局,湖北武汉430010 [2]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

出　　处：《水科学进展》2013年第1期103-110,共8页Advances in Water Science

基　　金：国家重点基础研究发展计划(973)资助项目(2012CB417001);中央高校基本科研业务费专项资金资助项目(206275798)~~

摘　　要：复杂边界下的流场数值模拟常基于非结构化网格进行求解,建立一种在非结构混合网格上求解水深平均的二维浅水方程的模型,以便精确模拟复杂边界、提高计算效率。该模型时间项离散采用隐格式使得模型具有较好的稳定性,对流项和扩散项分别采用总变差减小(Total Variation Diminishing,TVD)格式和构造辅助点的方法来离散,同时采用水深平均的标准k-ε模型来封闭湍流模型。选用两个经典验证算例检验模型,计算结果表明,基于非结构混合网格开发的模型具有较高的精度,且收敛性能较好。Unstructured grids are usually adopted in the solution of complex boundary flows. In this study, a depth- averaged two-dimensional （2-D） flow model is developed for mixed unstructured grids. The model uses both triangular cells and quadrilaterals, which ensures an accurate representation of irregular boundaries and at the same time, achie- ving a high computational efficiency. The unsteady term in the 2-D shallow water equations is treated implicitly. While the convection and diffusion terms are respectively approximated using the TVD （Total Variation Diminishing） algorithm and the auxiliary-point method. The depth-averaged standard κ-ε model is used for turbulent closure. Two classical test cases are chosen for model verification. The first one is a 2-D diversion flow case, and the second is a 90 degree bend-flow case. Results show that the proposed model performs well in terms of accuracy and presents good convergence characteristics.

关 键 词：非结构网格 混合网格 TVD格式 浅水方程 

分 类 号：TV131[水利工程—水力学及河流动力学]