承压含水层非稳定流拉普拉斯变换有限层分析

Laplace Transform Finite Layer Method for groundwater unsteady flow in a confined aquifer

以有限层法为基础,利用拉普拉斯变换,将时间域上的地下水非稳定流的问题转化到拉普拉斯域求解,从而提出了求解地下水三维非稳定流的拉普拉斯变换有限层法。建立了拉普拉斯空间中的有限层方程。在求得拉普拉斯空间解的基础上,利用Stehfest数值逆变换方法实现了一步求解给定时刻任意位置的地下水降深。在数值算例验证本文方法的合理性的基础上,讨论了Stehfest数值逆变换中计算项数K的合理取值和计算参数对K取值的影响。本文方法不仅将三维问题简化为一维问题求解,而且克服了传统数值方法只能对离散点分别进行数值逆变换的局限性,进一步提高了计算效率。

Based on Finite Layer Method and the Laplace transform,the problem of unsteady groundwater flow in time domain is transformed into Laplace space and a Laplace Transform Finite Layer Method（LTFLM） is presented to solve the three-dimensional unsteady groundwater flow problems.The finite layer formulations are developed to deduce the solution in Laplace space,and then the drawdown at any given time and at arbitrary point can be obtained by using numerical inversion of Stehfest algorithm with one step.The validity of this method is verified by a numerical example.The rational value of the number K in Stehfest numerical inversion and the influence of parameters on the selection of K are discussed.The LTFLM not only simplifies the three-dimensional problem into one-dimensional problem,but also overcomes the shortcoming of single-point numerical inverse.The efficiency of computation is remarkably improved.