基于修正Roe格式的有限体积法求解二维浅水方程

Finite volume model for the 2D shallow water equations using modified Roe scheme

应用迎风有限体积法,对具有复杂地形的二维浅水方程进行数值模拟.基于非结构化网格,采用Roe格式的近似Riemann解计算非粘性界面通量.底坡源项采用简单的斜底模型离散,从而保证了地形的离散精度.为了保证该计算格式的压力项和底坡源项的和谐性,对经典的Roe格式计算数值通量中的静水压力项进行了修正,并证明了修正后的Roe格式具备和谐性.通过与超临界流倾斜水跃和有激波混合流算例理论解结果比较,验证了该模型具有良好的间断捕捉能力、计算稳定性和守恒性.

A numerical model for finite volume method is developed for two-dimensional shallow-water flow with complicated geometry and topography. Based on the unstructured grid, the Roe＇s approximate Riemann solver is used for the computation of inviscid numerical flux functions. The bed slope source terms are computed by three vertices bottom value of a triangle lie on the same plane. Therefore, the discrete accuracy of landform is guaranteed. In order to balance the pressure terms with the bed slope source term for arbitrary geometry with triangular mesh, the classical Roe scheme is improved. The improved Roe scheme is confirmed to be well balanced by algebraic manipulation. The validity of the proposed modeling method is verified by the oblique shock wave and the transcritical flow with a shock numerical example.