A Novel Spacetime Boundary-Type Meshless Method for Estimating Aquifer Hydraulic Properties Using Pumping Tests

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 by solving the inverse boundary value problem in the spacetime domain. The effectiveness of this method was demonstrated through validation with the Theis solution, which involves transient flow to a well in an infinite confined aquifer. The study included numerical examples that predicted drawdown at various radial distances and times near pumping wells. Additionally, an iterative scheme, namely, the fictitious time integration method, was employed to iteratively determine the hydraulic properties during the pumping test. The results indicate that this approach yielded highly accurate solutions without relying on the conventional time-marching scheme. Due to its temporal and spatial discretization within the spacetime domain, this method was found to be advantageous for estimating crucial hydraulic properties, such as the transmissivity and storativity of an aquifer.

Deep Neural Networks with Spacetime RBF for Solving Forward and Inverse Problems in the Diffusion Process

“…By following the steps outlined in the proposed DNN with spacetime RBF architecture, numerical approximations can be obtained, as expressed below: (10) where net h represents the approximations, and j β represents the weights related to the output layer. The DNN architecture is illustrated in Figure 3, with the links between nodes symbolizing the weighted values responsible for managing signal transmission.…”

“…Numerical techniques like finite difference, finite element, spectral, or meshfree methods are commonly used [8,9]. Among these methodologies, the meshfree methods have attracted the attention of researchers from various scientific fields due to their ability to handle diffusion equations with complex and irregular geometries [6,8,10]. The radial basis function (RBF) collocation method is a meshfree approach used to analyze governing equations, where the unknowns are represented by function approximation.…”