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

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Published: Dec 26, 2023
DOI: https://doi.org/10.53555/jaz.v44iS8.4098
Keywords:
Burgers' Equation, Modified Crank–Nicolson Method, Nonlinear Partial Differential Equations, Fluid Dynamics

Main Article Content

Tejaskumar Sharma
Dr. Shreekant Pathak
Gargi Trivedi

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.


 

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How to Cite
Tejaskumar Sharma, Dr. Shreekant Pathak, & Gargi Trivedi. (2023). Numerical Modeling of Fluid Flow Through Porous Media: A Modified Crank-Nicolson Approach to Burgers’ Equation. Journal of Advanced Zoology, 44(S8), 363–371. https://doi.org/10.53555/jaz.v44iS8.4098
Issue
Vol. 44 No. S8 (2023): Mathematics and Applied Sciences
Section
Articles
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This work is licensed under a Creative Commons Attribution 4.0 International License.

Author Biographies

Tejaskumar Sharma

Department of Mathematics, N V Patel College of Pure and Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidhyanagar-388120, India. 

Dr. Shreekant Pathak

Department of Mathematics, N V Patel College of Pure and Applied Sciences, The Charutar Vidyamandal University, Vallabh Vidhyanagar-388120, India

Gargi Trivedi

Department of Applied Mathematics, Faculty of Technology & Engineering, The Maharaja Sayajirao University of Baroda, Vadodara, India, 

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