土壤溶质异常输运的时间分数阶对流扩散模型

A Time-Fractional Advection-Diffusion Model for Anomalous Diffusion of Solute in Soil

土壤系统经常表现出复杂的性质并导致溶质迁移的异常扩散。基于Skaggs等人的模型,本文研究开发蒸腾和根系吸水条件下的时间分数阶对流扩散方程(FADE)模型,以模拟根区的异常扩散并进行解析求解。模拟表明,时间分数阶对流扩散模型与整数阶对流扩散模型的数值结果在表面土壤附近出现偏差,随后随着时间的推移逐渐向下移动,偏差随深度逐渐扩大,较小的α对应较高的浓度曲线,说明土壤中溶质储层较强,导致溶质运移速度较慢,即存在亚扩散。Soil systems often exhibit complex properties and lead to abnormal diffusion of solute transport. Based on the model of Skaggs et al., this paper develops a time fractional advection-diffusion equation (FADE) model under transpiration and root water absorption conditions to simulate abnormal diffusion in the root zone and solves it analytically. The simulation shows that the numerical results of the time fractional advection-diffusion model and the integer advection-diffusion model deviate near the surface soil, and then gradually move downward with time. The deviation gradually expands with depth, and the smaller one corresponds to a higher concentration curve, indicating that the solute reservoir in the soil is strong, resulting in a slower solute migration rate, that is, there is sub-diffusion.