Numerical solution of advection-diffusion equation using finite difference schemes

Authors

  • LS Andallah Department of Mathematics, Jahangirnagar University, Savar, Dhaka-1342, Bangladesh
  • MR Khatun Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalgonj-8100

DOI:

https://doi.org/10.3329/bjsir.v55i1.46728

Keywords:

Advection-Diffusion Equation; Explicit scheme; Crank-Nicolson scheme; Relative error; Rate of convergence

Abstract

This paper presents numerical simulation of one-dimensional advection-diffusion equation. We study the analytical solution of advection diffusion equation as an initial value problem in infinite space and realize the qualitative behavior of the solution in terms of advection and diffusion co-efficient. We obtain the numerical solution of this equation by using explicit centered difference scheme and Crank-Nicolson scheme for prescribed initial and boundary data. We implement the numerical scheme by developing a computer programming code and present the stability analysis of Crank-Nicolson scheme for ADE. For the validity test, we perform error estimation of the numerical scheme and presented the numerical features of rate of convergence graphically. The qualitative behavior of the ADE for different choice of the advection and diffusion co-efficient is verified. Finally, we estimate the pollutant in a river at different times and different points by using these numerical scheme.

Bangladesh J. Sci. Ind. Res.55(1), 15-22, 2020

Downloads

Download data is not yet available.
Abstract
97
PDF
53

Downloads

Published

2020-04-21

How to Cite

Andallah, L., & Khatun, M. (2020). Numerical solution of advection-diffusion equation using finite difference schemes. Bangladesh Journal of Scientific and Industrial Research, 55(1), 15–22. https://doi.org/10.3329/bjsir.v55i1.46728

Issue

Vol. 55 No. 1 (2020)

Section

Articles

License

Bangladesh Council of Scientific and Industrial Research (BCSIR) holds the copyright to all contents published in Bangladesh Journal of Scientific and Industrial Research (BJSIR). A copyright transfer form should be signed by the author(s) and be returned to BJSIR.

The entire contents of the BJSIR are protected under Bangladesh Council of Scientific and Industrial Research (BCSIR) copyrights.

Creative Commons Licence
BJSIR is an open access journal, and articles are distributed under the terms of the Creative Commons Attribution-NonCommercial License (CC BY-NC) Creative Commons Attribution-NonCommercial 4.0 International License which allows others remix, tweak, and build upon the articles non-commercially, and although their new works must also acknowledge and be non-commercial, they don’t have to license their derivative works on the same terms.