非饱和土壤中水分和溶质同步运移的分数阶导数建模

Simulation and prediction of simultaneous water flow and solute transport in unsaturated soils is an important research topic in vadose zone research. The main challenge is due to the geometrical and physical heterogeneity of soils, and the intrinsic scale effect. The traditional Darcy’s law and Fick’s law cannot well describe the water movement and solute diffusion processes respectively, especially the heavy-tailed phenomena and the Non-Gaussian distribution of water content or solute concentrations exhibited in the experimental data of water flow and solute transport. Though the improved models have made progress in experimental data fitting and mechanism analysis, the key problems including parameter estimation, physical mechanism analysis and transfer of simulation results between different scales, have not been solved. This study aims to solve the above challenges by extending my research work in the last eight years. The first objective of this proposal is to establish a fractional-order derivative model to describe simultaneous water flow and solute transport in unsaturated soils, and characterize the heavy-tailed phenomena and Non-Gaussian distribution of solute concentrations. The second objective is to explore the mechanism of transport and determine the model parameters by using the particle random motion simulation in various fractal structures. Last but not least, this study will investigate the scale effect and verify the efficiency of proposed models, by conducting laboratory experiments and field observations. The final goal of this study is to develop a mathematical-physical model with clear physical mechanism and easy-to-get parameters to accurately characterize the simultaneous water flow and solute transport, and achieve the transfer of simulation results between different scales.

非饱和土壤中水分和溶质同步运移过程模拟和预测是非饱和带研究的重要研究课题之一。其主要困难来源于土壤几何和物理属性的非均匀性、运移过程的尺度效应。经典的达西定律和菲克扩散定律不能准确地描述非饱和土壤中水分运动和溶质扩散过程，特别是水分和溶质运移实验表现出的拖尾现象和非高斯统计分布特征。尽管已有的改进模型在实验数据拟合和机理分析方面取得了进展，但依然存在参数估计困难、物理机理不清晰和不同尺度结果不能相互转化的难题。基于申请者近八年来的研究工作，本项目拟发展分数阶导数模型，准确地描述非饱和土壤中水分和溶质同步运移过程，刻画浓度分布的拖尾现象和非高斯统计分布特征；采用分形结构中粒子随机运动模拟探明运移机理，确定模型参数；最后结合室内试验和野外观测探讨尺度效应机理，验证模型的有效性。目标是建立物理机理明确、参数估计简单、描述准确的数学物理模型，刻画同步运移过程，实现不同尺度模拟结果之间的转换。

非饱和土壤中溶质运移过程研究对土壤环境保护和土壤修复非常重要，但面临的问题也更复杂。由水动力弥散理论推导出来的符合费克定律的对流-弥散方程是研究土壤溶质运移的经典模型，但因为土壤的非均匀性，溶质运移过程本质上并不符合应用费克定律的前提条件。本项目利用分数阶导数模型刻画水分和溶质同步运移过程，并分析分数阶导数在水流和溶质运移过程中的演变机制；采用分形理论和随机行走模型相结合的思路，分析物理机理，确定分数阶导数模型参数；提出了模型的新算法（如求解时间分数阶扩散方程的半离散Kansa法，无网格方法等），实现了模型的长时间高精度模拟；新算法能够准确地描述溶质扩散过程，并预测长时间演化趋势；最后结合室内和野外试验确定相关土壤水力参数，验证模型的有效性，分析尺度效应。成果方面，团队成员基于上述研究内容，发表了期刊论文39篇，其中SCI检索论文38篇，综述论文1篇，软件著作权3项，专利7项。人才培养方面，依托项目培养了博士研究生5名，其中1名研究生已顺利获得博士学位。项目也极大地促进了项目组成员的学术交流，共资助学术会议17次，学术访问4次。综上所述，项目在土壤溶质反常扩散分数阶导数建模方面达到了预期目标，促进了科研团队的发展，培养了科研人才。