二维浅水明流的一种二阶高性能算法

A Second-Order High-Performance Algorithm for Two- Dimensional Unsteady Shallow Water Flow Computation

为了精确求解二维浅水方程组,在由任意三角形构成的无结构网格上建立了有限体积MUSCL算法,这是文献〔1〕中有限体积一阶Osher格式的一类二阶推广。通过采用预测校正二步时间积分和单元内引入坡度限制,该算法在时空上均可达到二阶精度.跨单元边界的法向数值通量采用通量向量分裂公式(FVS)计算。最后,通过长江口南支潮流计算和一维瞬时溃坝模型算例来说明该格式的优良性能及在浅水流动计算中的应用。

In order to solve the shallow water equations accurately, a finite-volume MUSCL scheme has been developed on an unstructured mesh consisting of arbitrary triangles. This scheme is a second-order extension of the first-order Finite-volume Osher scheme proposed in Ref. 1. Second-order accuracy both in time and space can be achieved by means of an explicit predictor-corrector scheme and slope-limiting within elements. Numerical flux in the direction normal to and across each side of elements is obtained by the flux-vector splitting approach (FVS). Finally, numerical results of tidal flow for the southern branch of the Yangtze estuary and of 1-D instantaneous dam-break-induced flow are presented, to illustrate the merits of this scheme in shallow-water-hydrodynamics and enable us to consider more com-plex applications.