Cheng-Yu Ku 1 and Chih-Yu Liu 2,*
1 School of Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan.
2 Department of Civil Engineering, National Central University, Taoyuan 320317, Taiwan.
* Correspondence: liu20452003@ncu.edu.tw
Abstract: This article introduces a new boundary-type meshless method designed for solving axisymmetric transient groundwater flow problems, specifically for aquifer tests and estimating hydraulic properties. The method approximates solutions for axisymmetric transient groundwater flow using basis functions that satisfy the governing equation through solving the inverse boundary value problem in the spacetime domain. The effectiveness of this method is demonstrated through validation with the Theis solution, which involves transient flow to a well in an infinite confined aquifer. The study includes numerical examples that predict drawdown at various radial distances and times near pumping wells. Additionally, an iterative scheme, the fictitious time integration method, is employed to iteratively determine the hydraulic properties during the pumping test. Results indicate that this approach yields highly accurate solutions without relying on the conventional time-marching scheme. Due to its temporal and spatial discretization within the spacetime domain, this method proves advantageous for estimating crucial hydraulic properties such as transmissivity and storativity of an aquifer.
Keywords: meshless, spacetime, pumping, hydraulic property, groundwater, aquifer.
https://doi.org/10.3390/math11214497