非统一结构网格下高精度溃坝水流数值模拟  

High-resolution numerical simulation of dam-break flow on non-uniform grids

作　　者：毕胜[1] 周建中[1] 刘懿[1] 张华杰 赵越[1] 

机构地区：[1]华中科技大学水电与数字化工程学院,武汉430074

出　　处：《水力发电学报》2014年第1期79-87,共9页Journal of Hydroelectric Engineering

基　　金：国家自然科学基金资助项目(51239004);水利部公益性行业科研专项(201001080;200901010)

摘　　要：针对溃坝洪水数值模拟面临复杂地形和不规则边界的特点,综合考虑了摩阻项和干湿界面对水流的影响以及模拟精度与运行效率等问题,建立了非统一结构网格下求解二维浅水方程的高精度Godunov型有限体积模型。基于局部Froude数,提出了水深-水位加权变量重构技术,有效模拟了复杂混合流和间断流,并结合Hancock预测-校正法提高了模型精度;引入了一种简单有效的处理方法模拟了运动的干湿界面变化;采用单元中心型底坡项近似处理方法并结合改进的半隐式格式,解决了摩阻项可能引起的刚性问题,提高了模型的稳定性。经典型算例和漳河水库溃坝洪水分析结果表明该模型稳定、精度高且和谐性强。A high-performance Godunov-type finite volume model was developed by solving the two-dimensional shallow hydrodynamics on non-uniform girds for application to dam-break flood propagation over complex topography, focusing on simulation efficiency and calculations of source terms and moving wet/dry fronts. In this model, a weighted surface-depth gradient method which considers the local Froude number, is adopted for water depths reconstruction, and the Hancock predictor-corrector method for time stepping. A simple but effective method is described for modeling wetting and drying. The central approximation for the central bed slope source term combined with a semi-implicit scheme for the friction terms can effectively prevents numerical instability of small depth calculations. Numerical results from test examples show that the new scheme is stable, precise and well-balanced.

关 键 词：水力学 数值模拟 非统一结构网格 水深 水位加权变量重构技术 干湿界面 

分 类 号：TV131.4[水利工程—水力学及河流动力学]