三角形网格下求解二维浅水方程的和谐Godunov格式

Well-balanced Godunov-type scheme for 2D shallow water flow with triangle mesh

为保证计算格式的和谐性,通过特殊的底坡源项处理技术,在三角形网格上建立了求解二维浅水流动方程的具有空间二阶精度的Godunov格式。应用准确Riemann解求解法向数值通量,用改正的干底Riemann解处理动边界问题。经典型算例和钱塘江河口涌潮计算验证,表明模型健全,分辨率高,具有较大的推广应用价值。

In order to establish a special well-balanced scheme technique for dealing with source term due to bottom topography constructed, this paper develops a well-balanced Godunov-type scheme of the second-order accuracy for 2D shallow water flow with triangle mesh. The numerical flux of the interface between cells are computed by the exact Riemann solver, and the improved dry Riemann solver is used to deal with wet/dry problem. The model is verified to compute some typical examples and the tidal bore on the Qiantang river. The results show that the scheme is robust and accurate, and worthy to be brought into wide use.