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在弥散核函数为负幂率函数的前提条件下,对传统的二阶对流—弥散方程进行非局域处理,推导出了分数阶对流—弥散方程,方程中的弥散项是分数阶微分.该方程柯西问题的格林函数解为一L啨vy分布密度函数,由此得到了一个包含3个参数的描述多孔介质中溶质运移行为的解.将所得到的L啨vy分布解用于模拟某一弥散试验中一空间点的溶质浓度的时间变化过程,模拟结果与实测结果吻合良好,很好地解释了实测结果的偏态和拖尾现象.而传统的二阶对流—弥散方程的高斯分布解却没有这些特征,不能解释偏态和拖尾现象.所得结果表明分数阶对流—弥散方程比传统的二阶对流—弥散方程能更好地描述多孔介质中的溶质运移行为.
Under the condition that the diffusion kernel function is a negative power rate function, the traditional second-order convection-dispersion equation is processed non-local and the fractional convection-dispersion equation is deduced. The dispersive term in the equation is fractional differential. The Green’s function of the equation Cauchy’s problem is solved by a L 啨 vy distribution density function, thus a solution containing three parameters describing solute transport behavior in porous media is obtained. The resulting L 啨 vy distribution solution is used to simulate The time varying course of solute concentration in a space experiment in a certain diffusion experiment shows that the simulation results are in good agreement with the measured results, which well explains the skewness and tailing phenomenon of the measured data. However, the Gaussian The results show that fractional convection-dispersion equation can describe the solute transport behavior in porous media better than the traditional second-order convection-diffusion equation.