中文摘要：

针对常系数对流扩散方程,基于微分算子分裂算法思想,分别对对流步与扩散步运用待定系数法,以格式的数值振荡和数值扩散最小为目标,得出各节点的权重系数,并在格式中引入无因次系数.用对流步进行计算,并将其结果作为已知值运用到扩散步的求解中,构造出一种新的一维对流扩散方程的数值求解格式.数值试验表明,相比其他已有格式,该格式可有效控制格式的数值振荡和数值扩散问题,易于编程,精度高,数值结果令人满意,较好地实现物质输移扩散的真实物理过程.

英文摘要：

A new method is developed with the differential operator splitting algorithms and the undetermined coefficient method to solve one-dimensional convection-diffusion equation,which has attracted attention because of its importance.With the target of numerical oscillation of the least numerical oscillation and numerical proliferation,the method gets weight index of each node and introduces a dimensionless coefficient.Calculating by convection and applying its results as known value to the solution of step-proliferation.The results of numerical experiments show that compared with other existing schemes,the scheme can control the numerical oscillation and proliferation more effectively and has higher accuracy.The scheme proposed can simulate the real physical process of material transport and diffusion.