土壤和裂隙介质中反常扩散的分数阶变导数建模

项目名称： 土壤和裂隙介质中反常扩散的分数阶变导数建模

项目编号： No.11202066

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 孙洪广

作者单位： 河海大学

项目金额： 24万元

中文摘要： 自然环境土壤和裂隙介质中污染物迁移过程是污染预测和治理的一个重要应用基础研究课题。大量的实验和现场观测发现这些迁移过程一般不符合Fick第二定律，是一类反常扩散。近年来分数阶导数扩散方程已成功应用于描述此类反常扩散现象。但是常规的分数阶扩散模型仅考虑介质的非均质性，未涉及介质结构或孔隙率随时空变化的影响，此外，有关的机理实验也鲜有报道。基于申请者近5年来的研究工作，本项目拟发展分数阶变导数扩散模型，反映介质非均质性的时空变化对扩散行为的影响；采用溶质迁移机理实验与数值模拟相结合的方法，探明模型阶数与介质结构的关系。从变导数的物理意义入手，结合非Fick扩散特征分析，研究土壤和裂隙介质中溶质迁移演化的机理。本项目的目标是建立物理机理明确，参数估计简单的变导数对流-扩散方程模型，刻画污染物浓度的演化趋势和主要特征，评价污染物对水环境的长期影响，为复杂环境中水污染预测和治理提供力学理论模型。

中文关键词： 反常扩散；尺度变换；分数阶变导数；半离散有限单元法；参数估计

英文摘要： Contaminant transport in natural soil and fractured media is an important topic of applied research in pollution prediction and control.Numerous experimental and field observations have found that such transport in general do not obey Fick's second law and is of anomalous diffusion. In recent decades, fractional derivative diffusion models have been successfully applied to anomalous diffusion of this type. However, these fractional models only consider the heterogeneity of medium and do not involve the influence of temporal and spatial variations of medium structures or porosity. Moreover, little experiment has been done and reported concerning their mechanism in literature.Based on my research work in recent five years, the objective of this proposal is to establish a variable-order fractional diffusion model to describe contaminant transport in such varying soils or fractured media. We will combine lab experiments and numerical modeling to explore underlying physical mechanism. The key point is the analysis of non-Fickian feature via the physical significance of fractional variable-order derivative and then investigates mechanism underlying solute transport in soils and fractured media. The purpose is to develop a variable-order fractional advection-diffusion equation model with clear physical mechanism and ea

英文关键词： Anomalous diffusion；Scale transfer；Variable-order fractional derivative；Semi-discrete finite element method；Parameter estimation