Numerical Modeling of Fluid Flow Through Porous Media: A Modified Crank-Nicolson Approach to Burgers' Equation

Abstract

This study presents a numerical modeling approach to investigate fluid flow through porous media, focusing on the application of the Modified Crank-Nicolson method to solve the Burgers' equation. The Burgers' equation, known for capturing non-linear features in fluid dynamics, serves as a pertinent model for porous media flow. The Modified Crank-Nicolson method, a variation of the traditional Crank-Nicolson technique, renowned for its stability and accuracy in solving parabolic partial differential equations, is employed to simulate the temporal evolution of fluid flow within the porous medium. Numerical experiments are conducted to explore the dynamic behavior of the system, considering various parameters and boundary conditions. The results showcase the efficacy of the Modified Crank-Nicolson approach in providing insights into the complex phenomena associated with fluid flow through porous media. This research contributes to the broader understanding of numerical methods in porous media dynamics and establishes a foundation for further investigations in related fields.