复杂地形上非恒定浅水二维流动数值模拟  

Numerical modeling of two-dimensional shallow water flows over complex topography

作　　者：毕胜[1] 周建中[1] 张华杰 宋利祥[1] 陈生水[2] 

机构地区：[1]华中科技大学水电与数字化工程学院,武汉430074 [2]南京水利科学研究院,南京210029

出　　处：《水动力学研究与进展（A辑）》2013年第1期94-104,共11页Chinese Journal of Hydrodynamics

基　　金：高等学校博士学科点专项科研基金(20100142110012);水利部公益性行业科研专项基金(201001080;201001034;200901010)~~

摘　　要：该文针对复杂地形条件下浅水流动数值模拟在干、湿边界附近面临计算失稳和格式和谐性差等难题,建立了非统一结构网格下二维浅水方程的高精度、高分辨率的有限体积模型。以基于水位的改进浅水方程为水流控制方程,采用能够有效捕获激波的HLLC近似黎曼算子计算界面通量;采用MUSCL-Hancock预测-校正法获得了在空间和时间上都具有二阶精度的Godunov格式;通过构造底坡修正项,保证了计算格式的和谐性;采用改进的半隐式格式解决摩阻项可能引起的刚性问题,提高了格式的稳定性。并通过算例研究,结果表明,该模型具有很好的和谐性与稳定性,适应干、湿界面计算,能有效模拟复杂地形条件下的水流运动。This paper presented a high-resolution two-dimensional finite-volume numerical model on structured but non-uniform grids for Unsteady two-dimensional shallow-water flow over complex topography. The HLLC approximate Riemann solver was utilized because it is suited to cases involving a wet-dry interface. Overall second order accuracy in space and time was achieved using a two-step unsplit MUSCL -Hancock method. To alleviate the problems associated with numerical instabilities, the friction source terms were treated in a partly implicit way. Finally, three tests were used to validate the solver of the present model and the results indicated that present model may simulate irregular topography accurately and stably.

关 键 词：浅水方程 源项 非统一结构网格 HLLC MUSCL-Hancock 

分 类 号：TV131.2[水利工程—水力学及河流动力学]