激波捕捉格式求解复杂床面浅水方程的源项处理

为了解决激波捕捉格式应用于浅水模拟所带来的源项,尤其是底坡项的处理这一难点问题,建立了一种边界条件给定简单的方法。采取构造单元内部流动变量分布的手段,避开了对底坡项的直接处理,综合了常用的Godunov型通量差分裂格式(flux difference splitting,FDS)和LeVeque波传播方法的思想。通过与"人工渗透法"相结合,该方法被应用于存在移动的干湿边界的情况。对两个有解析解和一个有实验观测数据的算例进行了模拟,模拟结果与解析解或观测数据吻合良好。该方法可有效处理复杂地形变化的二维浅水流动。

Treatment of source terms in shock-capturing schemes for shallow-water equations over complex bed topographies

A method was designed to reconstruct the cell variables to avoid direct calculation of the source terms,especially the bed topography term,in high-resolution schemes used to simulate 2-D shallow-water flows.The model uses the Godunov-type flux difference splitting(FDS)scheme and LeVeque's wave propagation algorithm with the artificial porosity method to model wetting and drying of 2-D shallow water flows.The boundary conditions are easily specified.The model was used to analyze three typical problems with excellent agreement obtained between the simulations and analytical solutions or field data.The results indicate that the method can accurately and efficiently simulate shallow-water flows over complex bed topographies.