对流方程解的高价数值格式  

A higher order numerical method for pure advection transport

作　　者：杨国录[1] J.A.Cunge 

机构地区：[1]武汉水利电力学院 [2]法国水力学实验室

出　　处：《水利学报》1989年第10期9-18,共10页Journal of Hydraulic Engineering

摘　　要：本文对经典对流方程的数值解建立了一个高阶数值格式。原理是在特征线脚所在网格的两个基点上建立5阶插值多项式,此多项式考虑了一阶导数的对流和两阶导数的嵌入,进而使数值格式的截断误差可达近6阶。理论分析和模拟单波对流输移验算结果表明,此格式比Holly-Preissmann方法具有更高的精度。A new higher order accurate method is presented for pure advection transport in one-dimensional flow. Following the method of characteristics, the interpolation of the concentration at the foot of the characteristic is carried out by a fifth-degree polynomial. The latter is constructed by using the concentration and its first and second derivatives at computational points on current time level tas informations. Then the concentration and its first derivative are both transported by advection along characteristic curve towards t + △t time level, the second derivative is obtained at new t+△t time level by the resolution of a linear system of equations. The approximation of the method is of the sixth order. Formal error analysis of the method and comparisons with analytical solution demonstrate its excellent accuracy.

关 键 词：对流方程 高阶数值格式 数值解 

分 类 号：TV131.4[水利工程—水力学及河流动力学]