复杂介质中地下水污染物反常扩散分数阶模型构建研究：基于等待时间外势依赖随机游走理论

Groundwater pollution has been a threat to human survival and development seriously,so we need to study groundwater contaminant transport in complex porous mediums to provide powerful theoretical basis for predicting and controlling groundwater pollution. Considering the effect of external potential variation during the anomalous migration of groundwater contaminant in complex porous mediums, we derive the general external potential dependent fractional advection-dispersion equation based on the continuous time random walk model in which the waiting times depend on the external potential. Furthermore,to describe the chemical dynamic behavior of groundwater chemical contaminants in complex porous medium, we will introduce a general model:the external potential dependent fractional advection-dispersion-reaction equation by using the ways proposed by Yuste for describing anomalous chemical dynamic behavior and analyze the influence of external potential change on the solutions of the equations by contrasting the numerical simulation results.

地下水污染已对人类的生存与发展造成严重威胁，迫切需要研究复杂多孔介质中地下水污染物迁移机制为预测、防治地下水污染提供有力理论依据。考虑复杂多孔介质中地下水污染物反常迁移时外势能变化产生的影响，我们将基于粒子跃迁等待时间依赖于外势能的连续时间随机游走理论，建立具有外势依赖的分数阶对流-弥散方程。为进一步揭示复杂多孔介质中地下水化学污染物的化学动力学行为，我们将运用Yuste等研究反常扩散效应下物质化学反应行为的相关理论，建立具有外势能依赖的分数阶对流扩散反应方程，并通过数值模拟分析外势能变化对方程解的影响。