交错网格下的浅水方程高分辨Gauss型格式

在交错网格上,基于高精度的Gauss积分公式,针对浅水波方程设计了对模拟涌波具有高分辨率的完全二阶精度的数值计算格式。由于采用了交错网格,差分格式不需要解Riemann问题,因此本文格式具有计算简单、工作量少、编程简便等特点。另外,在一维单个方程时,本文格式在CFL(Courant Friedrich Lewy)条件限制下为TVD(Total Variation Diminishing)格式,在二维和三维情况下格式具有MmB(Maximum and Minimum Bounds Preserving)性质。利用国家高性能计算中心(合肥)的曙光1000型分布存储大规模并行机,对在交错网格下所构造的求解浅水方程的高分辨差分格式进行了并行实现,几个算例的计算结果令人满意。

A high resolution Gauss scheme with staggered grid for shallow water equation

Based on the high accurate Gauss integral formula,a high resolution and totally two orders accurate scheme is designed by using a staggered grid for shallow water equation.The difference scheme does not face to solve Riemann problem due to use the staggered grid,so the difference scheme has the specialty of simple computing and convenient programming.By the way,in one-dimensional scalar equation,the difference scheme is TVD (Total Variation Diminishing scheme) with CFL (Courant Friedrich Lewy) condition.In two- and three-dimensional cases,the scheme has MmB (Maximum and Minimum Bounds Preserving) property.With the Shuguang-1000 distribution storage vast scale parallel computer at the computing center of China,the high resolution difference scheme for solving shallow water equation with the staggered grid is used to numerical simulate several typical program,the computed results are satisfy.