时变边界一维对流弥散方程解析解及其在土柱试验中的应用

Analytic solution for 1D convection-dispersion equation with time-variable boundary and its application in soil column experiment

运用格林函数法,推导了一维有界时变边界对流弥散-线性耗散方程的解析解,然后将其与数值模拟结果对比,并分别应用于土柱热传导和溶质运移试验。结果表明:初始条件及上、下边界条件的贡献量相互独立,并且初始条件的影响随时间衰减,最终消失;解析解能很好地匹配数值模拟结果、土柱试验实测土温变化和溶质穿透曲线。

This study derived an analytical solution of 1D convection-dispersion-linear dissipation equation with variable boundary using the Green's function method,then compared the analytical solution with the numerical solution,and after that applied it to the heat conduction and solute transport experiments of a soil column.Results showed that the contributions of initial,upper and lower boundary conditions were independent.At the same time,analytical results matched the numerical simulation and the observed results of experiments well.As a conclusion,the analytical solution can represent the heat conduction and solute the transport processes well.