Providing a Numerical Method for Solving Groundwater Equations

Network methods are one of the most widely used groundwater modeling tools that have become widespread and popular in the last two decades. On the other hand, advances in the computing power of computers and their ease of access have led to the rapid development of numerical methods for solving groundwater problems. In this study, with a new approach to network methods, these methods are introduced as a numerical model to simulate the movement of groundwater. The first step in estimating groundwater behavior is to obtain a mathematical model. According to Darcy's law and the establishment of mass conservation, it can be shown that the equation governing groundwater in stable conditions is the Laplace equation. Therefore, by obtaining the physical properties of the desired aquifer using the experiment and understanding the boundary conditions governing that aquifer, a complete mathematical model governing the desired problem can be obtained. Unfortunately, since the physical properties of the problems in nature are not homogeneous and the boundaries of the problems under study are geometrically irregular, it is impossible to solve these problems analytically. To do so, researchers have been using numerical and laboratory methods for years. All numerical methods for solving the Laplace equation first decompose the scope of the problem in the sense that they either divide it into multiple nodes or into multiple elements and then use mathematical methods. In this article, a new approach is to find algebraic relations between those different nodes or elements. In other words, after parsing the scope of the problem, they turn the Laplace equation into a system of linear equations.

Keywords:

Algebraic Relations , Network Methods , Darcy' s Law , Numerical methods