Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation
In the present article, the advection-diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative...
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American Society of Mechanical Engineers
2019
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author | Singh, Anup Das, Subir Ong, Siew Hui Jafari, Hossein |
author_facet | Singh, Anup Das, Subir Ong, Siew Hui Jafari, Hossein |
author_sort | Singh, Anup |
collection | UM |
description | In the present article, the advection-diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method. © 2019 by ASME. |
first_indexed | 2024-03-06T05:59:50Z |
format | Article |
id | um.eprints-23425 |
institution | Universiti Malaya |
last_indexed | 2024-03-06T05:59:50Z |
publishDate | 2019 |
publisher | American Society of Mechanical Engineers |
record_format | dspace |
spelling | um.eprints-234252020-01-14T04:10:46Z http://eprints.um.edu.my/23425/ Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation Singh, Anup Das, Subir Ong, Siew Hui Jafari, Hossein QA Mathematics In the present article, the advection-diffusion equation (ADE) having a nonlinear type source/sink term with initial and boundary conditions is solved using finite difference method (FDM). The solution of solute concentration is calculated numerically and also presented graphically for conservative and nonconservative cases. The emphasis is given for the stability analysis, which is an important aspect of the proposed mathematical model. The accuracy and efficiency of the proposed method are validated by comparing the results obtained with existing analytical solutions for a conservative system. The novelty of the article is to show the damping nature of the solution profile due to the presence of the nonlinear reaction term for different particular cases in less computational time by using the reliable and efficient finite difference method. © 2019 by ASME. American Society of Mechanical Engineers 2019 Article PeerReviewed Singh, Anup and Das, Subir and Ong, Siew Hui and Jafari, Hossein (2019) Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation. Journal of Computational and Nonlinear Dynamics, 14 (4). 041003. ISSN 1555-1415, DOI https://doi.org/10.1115/1.4042687 <https://doi.org/10.1115/1.4042687>. https://doi.org/10.1115/1.4042687 doi:10.1115/1.4042687 |
spellingShingle | QA Mathematics Singh, Anup Das, Subir Ong, Siew Hui Jafari, Hossein Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title | Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title_full | Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title_fullStr | Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title_full_unstemmed | Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title_short | Numerical Solution of Nonlinear Reaction–Advection–Diffusion Equation |
title_sort | numerical solution of nonlinear reaction advection diffusion equation |
topic | QA Mathematics |
work_keys_str_mv | AT singhanup numericalsolutionofnonlinearreactionadvectiondiffusionequation AT dassubir numericalsolutionofnonlinearreactionadvectiondiffusionequation AT ongsiewhui numericalsolutionofnonlinearreactionadvectiondiffusionequation AT jafarihossein numericalsolutionofnonlinearreactionadvectiondiffusionequation |