中文摘要：

建立了适应于结构网格的复杂边界浅水流动有限体积数学模型。基本控制方程采用对自由水面相对高度在水平向和垂直项进行分裂后形成的守恒性的修正二维浅水方程,在结构网格上采用中心型格式离散基本控制方程,采用能够有效捕捉激波的近似黎曼求解器HLLC计算界面通量,并使用坡度限制器重构界面两侧变量,利用MUSCL-Hancock在时间维上积分,使时空精度提升到二阶;分别采用中心差分格式和全隐式方法处理底坡项和阻力项,保证了模型稳定性。提出了局部修正底高和水位的干湿边界处理方法和基于B样条曲线的复杂边界处理方法,很好地处理了急变水流变化引起的干湿单元网格的动态交替和复杂边界处水流特性正确表达。最后通过算例证明了模型性能较好,具有推广价值。

英文摘要：

This paper presents a high-resolution two-dimensional finite-volume numerical model based on structured grids for unsteady two-dimensional shallow-water flow over topography with wetting and drying and complex boundary. This model adopts a modified version of the two-dimensional shallow water equations, which correctly balances flux gradient and source terms, and calculates flow flux with Godunov-type finite-volume shock-capturing HLLC schemes. Spatial and temporal accuracy are improved to second order by applying a slope limiter and a prediction-correction method called MUSCL-Hancock, and slope source terms and friction source terms are treated with central difference scheme and fully implicit method respectively. A robust procedure is adopted to efficiently and accurately simulate the movement of wet/dry boundary, and a method of high simulation precision for complex boundary, simplicity of treatment, and high calculation efficiency, is used for calculation of computational boundary. Finally, two tests are used to validate the solver of the model, and the results indicate that the presented model can accurately capture various flow processes and shows good stability and accuracy.