基于非结构网格的非恒定浅水二维有限体积数学模型研究

Unstructured grid finite volume model for two-dimensional shallow water flows

建立了基于非结构三角网格系统的非恒定浅水二维水流数学模型。基本控制方程采用浅水二维水流方程;采用能够有效捕捉激波的HLLC近似黎曼算子求解界面通量,并对界面变量进行数据重构,模型具有二阶精度;将地形高程定义在三角单元节点上,使得单元间地形连续变化,结合处理底坡的DFB(divergence form for bed slope source term)方法,保证了模型的和谐性,使其能够有效地模拟不规则地形条件上干湿边界变化过程中的水流过程;采用了隐式方法处理阻力项,从而保证了模型的稳定性。最后,通过四个经典算例对模型进行了系统地检验。结果表明:此模型具有很好的和谐性和稳定性,能够有效、准确地模拟复杂地形情况下水流运动,显示了广阔的应用前景。

This paper presents a high-resolution two-dimensional finite-volume numerical model based on unstructured grids for unsteady two-dimensional shallow-water flow over topography with wetting and drying. The bed elevation is defined at triangle grid nodes and bed slope source is solved by DFB （divergence from for bed slope source term） method, which balanced correctly the flux gradient and source terms in Godunov-type finite volume shock-capturing schemes and by the moving wet^try boundary as the flood rises or falls. To alleviate the problems associated with numerical instabilities due to small water depths near a wet/dry boundary, the friction source terms are treated in a fully implicit way. Finally, four testsare used to validate the solver of the present model. Results of the numerical simulation indicate that present model may accurately capture flow processes over irregular topography.