中文摘要：

溶质在多孔介质中的运移一般以对流与机械弥散为主，基于Fick扩散定律的对流弥散方程（ADE）是描述溶质运移行为模式的经典模型[18，24]．然而，上世纪90年代以来，有关研究[1,2，6，7，14，19，26]表明，用ADE模型来描述溶质的运移过程时，有时并不能很好的模拟穿透曲线的提前穿透或拖尾现象，同时也不能很好地解释溶质长距离传输中表现出的弥散系数的尺度效应等问题．事实上，ADE模型揭示了溶质运移的瞬时扩散性与对称性，但多孔介质中的溶质运移有时表现出明显的非对称性等非Fick扩散行为，分数阶微分方程逐渐发展为研究这种反常扩散行为模式的有力工具．

英文摘要：

This paper deals with numerical solution for one-dimensional non- symmetric fractional advection-dispersion equation （FADE in short） in a finite domain and parameters inversion. A difference scheme is presented based on the Griinwald-Letnikov definition of the fractional derivative, and sensitivity of the solution to the fractional order and the skew parameter is analyzed for different input sources. Furthermore, an inverse problem of determining the fractional or- der and dispersion coefficient simultaneously is investigated by final observations. Numerical inversions are carried out successfully by applying an optimal perturba- tion regularization algorithm, and impact of the fractional order on the inversion algorithm is discussed.