Simulating steady saturated groundwater flow using converging diverging pipe networks and its numerical solution

In this paper, porous media is modeled by a network of cylindrical and converging-diverging pipes which is then employed as a numerical tool to solve steady saturated groundwater flow. This model, similar to Finite Difference (FD) and Finite Element (FE) models, transforms the governing equation into a set of linear algebraic equations. It is shown that the coefficients of the obtained matrix are a function of how the pipes converge and diverge (curvature number). By solving three different examples, it is shown that curvature number of 8 and -0.30557 are equivalent to FD and FE respectively and curvature numbers within this range yield more accurate results compared to FD and FE methods. By increasing the number of meshes the curvature number minimizing the total error in the domain approaches 0.71508 in all examples. It is concluded that the proposed model may be considered as a novel numerical tool for solving steady saturated groundwater flow with higher accuracies and rates of convergence compared to traditional methods such as FD and FE. Moreover, since the construction of the matrix of the proposed method is much easier than FE and FD and in addition the model may be conceptualized much easier than traditional numerical methods, the proposed method may serve as an educational tool for numerical modeling and easily be employed by those who are not an expert in numerical techniques. © 2018 Begell House Inc.. All rights reserved.