一种新的海水渗流模型及其数值算法

A New Mathematical Model and Numerical Simulation for Sea Water Intrusion into Coastal Aquifers

反常扩散通常用于模拟物理、金融和水文等各种现象,整数阶扩散方程不能准确地模拟这类反常扩散过程.本文研究了溶质入侵地下水层的特征,建立了海水渗入地下水层的反常扩散模型,将整数阶的导数用分数阶导数来替换,利用差分离散建立此模型的数值算法,证明了算法的收敛性,并给出数值例子,通过计算机模拟表明算法的有效性.

Anomalous diffusion has been applied to many problems in physics ,finance and hydrology. Integer differential equations cannot correctly simulate the anomalous diffusion phenomena. In this paper, the characteristic of solutes transport in groundwater is described. We give a new mathematical model for saltwater intrusion into coastal aquifers replacing the integeral derivative by a fractional derivative. We derive the numerical algorithm for the mathematical model by using difference discrete. Convergence of the algorithm is proved. Finally, numerical example is presented to show the effectiveness of this algorithm.