污染浓度对流扩散的三节点高精度格式

Three-point scheme with high accuracy for the convection-diffusion equation of the pollutant concentration

通过局部区间级数展开的方法,构造了污染浓度对流扩散方程的任意N阶精度的三节点差分格式.数值求解得到各节点的值后,可由区域内的解析表达式计算区间内任意一点的值.在格式的形成过程中,只需求解N-2阶的三角方程,计算量小、简单,易编程.并对格式的稳定性做了分析,数值结果表明,格式的精度、效率都很高.

A threepoint scheme with high accuracy is presented in this paper to solve numerically the convectiondiffusion equation of the pollutant concentration. The novel and efficient scheme is obtained by the local expanding of Taylor series with N order. When the value at every grid are obtained by solve numerically the three diagonal algebra equations, the value at arbitrary point of the local space can be calculated in terms of a formula expressed by the grid value. The main features of this scheme are simple and small amount of the computation. the stability of the scheme is analysed by several examples. 