考虑吸附和降解时溶质在土壤中运移的对流-弥散模型及其准解析解  

Quasi-analytical solution for advection-dispersion model of solute transport through soils under steady state flow

作　　者：张德生[1] 张建丰[2] 沈冰[2] 

机构地区：[1]西安理工大学理学院 [2]西安理工大学水利水电学院,陕西西安710048

出　　处：《西北农林科技大学学报（自然科学版）》2009年第3期187-192,共6页Journal of Northwest A&F University(Natural Science Edition)

基　　金：国家自然科学基金项目(50779055;50779052)

摘　　要：【目的】了解吸附性溶质在土壤中的运移规律,为土壤溶质运移机理研究和应用提供理论支持。【方法】利用溶质运移的对流-弥散理论、Laplace变换、超几何方程和特征有限元法,对溶质在土壤中的运移规律进行理论研究和数值模拟。【结果】给出了稳定流条件下,考虑随深度变化的一阶降解和随深度变化的线性平衡吸附时,一维溶质运移的对流-弥散方程;在初始浓度为0,半无限一维空间内第一类边界条件下,推导出了溶质相对浓度的准解析表达式;用特征有限元法建立了相应的数值模型。【结论】对比数值解和准解析解的计算数据可以看出,本研究所得准解析解是正确的;同时,数值计算所产生的误差很小,所得数值模型能满足实际工作对计算精度的要求,可用于实际工作。[Objective] The study was to find the transport law of adsorbed solute in soils and to pro- vide theoretical basis for mechanism research and applications of solute transport through soils. [Method] The advection-dispersion theory, Laplace transform, hypergeometric equation and the characteristic finite element method were used for theory research and numerical simulation. [Result] The advection-dispersion model of 1-D solute transport through soils with depth-dependent first-order degradation and depth-de- pendent linear equilibrium absorption under steady state flow was studied,and a quasi-analytical solution describing the concentration distribution was deduced under the initial concentration zero and the first boundary condition of a semi-infinite 1-D space. The numerical model of the advection-dispersion model was constructed by the characteristic finite element method. [Conclusion] It can be seen from comparing the numerical solutions to the quasi-analytical solutions that the quasi-analytical solution is right and errors caused by the numerical computation are so small that the numerical model perfectly meets the demand of calculating precision in practical work.

关 键 词：溶质运移 对流-弥散方程 准解析解 特征有限元法 

分 类 号：S153.5[农业科学—土壤学]