求解半无限长多孔介质柱体水动力弥散系数的一种最小二乘法

The Least Square Method Gaining the Hydrodynamic Dispersion Coefficient of the Semi-infinite Pore Medium Sylinder

针对半无限长多孔介质柱体,一端为定浓度边界的水动力弥散反求参数问题,先用数值方法求解补余误差函数erfc(x)的反函数,再根据该问题的解析解,通过变量代换,构造一个基于解析解的最小二乘模型来反求水动力弥散系数。最后将该方法应用于一个实例,计算结果表明该方法比erfc(x)近似公式法、配线法、正态分布函数法等传统方法要好。

The article studies how to gain the hydrodynamic dispersion coefficient from the one-dimension dynamical dispersion model,in which the concentration in one end of the pore medium infinite sylinder is constant.Firstly,the inverse function of y=erfc（x） is solved by the numerical method,and then mathematic model,using least square method,is established through variable transformation,according to the the analytical solution.At last,with application of the method to solve the practical problem,the results show the method is better than the traditional methods,such as erfc（x） approximation formula,fitting curve method,normal distribution function method and so on.