无结构网格上二维浅水流动的数值模拟

Numerical Modelling of Two-Dimensional Shallow Water Flows on Unstructured Grids

提出在无结构网格上建立有限体积高性能格式族的统一框架，通过引入跨单元界面法向数值通量的逆风分解，将一维Ｏｓｈｅｒ、ＴＶＤ两种通量分裂格式自然地推广至二维浅水方程组。给出了各种情况下浅水方程组有限体积法边界处理的计算公式。最后，利用该格式对穹包溢流、陆地动边界和河口潮流三个问题进行计算。结果表明，这类守恒格式具有高精度、无振荡性以及处理复杂流态过渡、自动捕俘间断和模拟陆地动边界的功能。

This paper presents a frame of constructing a family of finite volume high performance schemes on unstrctured grids for solving the shallow-water equations.By introducing upwind decompositions of numerical fluxes in the direction normal to and across each side of cells,four one dimensional algorithms including Osher,TVD,and two Flux-Vector Splittings,can naturally be extended to the two dimensional case.Moreover,boundary procedures applied to opern and land boundaries for both supercritical and subcritical flows are given.Finally,the schemes have been used to model flows over a bump,with a moving land boundary, and of an estuay tide,respectively.The results show that they are not only sufficiently accurate and nonoscillatory,but also capable of treating automatically fow transients,hydraulic jumps,and moving land boundaries.