Introduction of the Network Method as a Numerical Method for Solving the Groundwater Equation

The present study examines and introduces the network method as a numerical method for solving the groundwater equation. The use of network models has grown significantly over the past decade. These models have been widely used in the fields of petroleum and environmental engineering. The application of the network model in recent years has not been limited to cases such as calculations related to two-phase flow or permeability calculations. New applications of this type of model include the study of three-phase flow, the effect of hysteresis, wettability, and mass transfer between different phases, which were mentioned in detail in the research background chapter. The purpose of this research is to use the network model as a numerical method for solving the groundwater equation in the saturated state, meaning that the problem in question is divided into different nodes using the network model and instead of solving the partial differential equation governing the problem, the equation governing the network model is solved. According to the equations obtained for homogeneous and homogeneous aquifers, the coefficients of different nodes depend only on their distance from the node in question and are proportional to the inverse of their distance. In the section investigating the effect of heterogeneity and asymmetry, the coefficients obtained, in addition to being proportional to the inverse of their distance, were also proportional to the fourth power of the pipe diameter. In order to be able to attribute the coefficients of the nodes only to the length in all cases, whether homogeneous and homogeneous or inhomogeneous and non-homogeneous porous media. The advantage of using equivalent length is that all node coefficients will be a function of their distance from the desired node only.

کلیدواژه ها:

Network model ، Environment ، Groundwater ، Saturation ، Partial Differential Equation