求解地下水流问题的混合拉普拉斯变换有限差分法

应用一种将拉普拉斯变换与有限差分法相结合的新方法——混合拉普拉斯变换有限差分法(HLTFDM),求解非稳定地下水流问题。首先使用拉氏变换除去控制方程中的时间导数项,接着在象空间用有限差分方法求解并采用Honig—Hirdes算法进行数值反演,得到原物理问题的解。算例表明,本文所使用的这一新算法稳定并收敛于精确解。由于计算过程中没有时间步长,因此,该方法是求解大区域长时间地下水流动态问题的有力工具。

Hybrid Laplace Transform Finite Difference Method for Transient Groundwater Flow Problems

The new method involving the combined use of the Laplace transform and the finite difference method is applicable to the problems of time—dependent groundwater flow. The present method removes the time derivative from the governing differential equation using the Laplace transform and then solves the associated equation with the finite difference method. The transformed groundwater head is inverted numerically by the algorithm of Honig and Hirdes to obtain the result in the physical quantities. Numerical examples show that the new method is stable and convergent to the exact solution. There exists notime step ,thus the present method is a useful tool in solving long time groundwater dynamic problems in large field domain.