一维对流弥散方程的显式差分法求解及其收敛性分析

Explicit Difference Method for One-Dimensional Convection Dispersion Equation and its Convergence Analysis

对一维对流弥散方程的特点进行全面分析,在稳定渗流场中,认为差分格式中的流速项系数和弥散系数是随空间节点的位置而改变的,给出了不同渗流方向下相应的差分格式,推导了对应的收敛条件,并考虑了边界浓度衰减的影响,引入边界衰减因子,最后将该方法运用到实际工况中。从计算结果中发现,在满足收敛条件的情况下,能够计算出浓度在时间和空间的变化数值,最终计算结果是收敛的,而不满足相应的收敛条件时,其计算结果是不收敛的。所介绍的方法能够求解一维对流弥散方程的解析解,简单实用,且能够方便了解每一迭代步内的浓度空间分布情况。

In this paper,some characteristics of one-dimensional convection-dispersion equation were comprehensively analyzed.In addition,it was considered that the velocity term coefficients and dispersion coefficients in the difference scheme vary with the location of spatial nodes.Besides,the corresponding difference schemes in different seepage directions were given,and the corresponding convergence conditions were also derived.Moreover,the effect of boundary concentration attenuation was considered.Finally,the method was applied to a practical case.It was found from the calculation results that when the convergence conditions were satisfied,the variation values of concentration in time and space could be calculated.Furthermore,the final results were convergent,but if the corresponding convergence conditions were not satisfied,the calculation results were not convergent.The method presented in this paper can solve the analytical solution of one-dimensional convection-dispersion equation.The method is simple and practical,and the spatial distribution of concentration in each iteration step can be easily understood.