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

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 boundcries 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.