Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters

Convection, diffusion, and reaction mechanisms are characteristics of transient mass-transfer phenomena that occur in natural and industrial systems. In this article, we contemplate a passive scalar transport governed by the convection-diffusion-reaction (CDR) equation in 2D flow. The efficiency of...

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Main Authors: Uzair Ahmed, Daoud Suleiman Mashat, Dalal Adnan Maturi
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2022/3476309
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author Uzair Ahmed
Daoud Suleiman Mashat
Dalal Adnan Maturi
author_facet Uzair Ahmed
Daoud Suleiman Mashat
Dalal Adnan Maturi
author_sort Uzair Ahmed
collection DOAJ
description Convection, diffusion, and reaction mechanisms are characteristics of transient mass-transfer phenomena that occur in natural and industrial systems. In this article, we contemplate a passive scalar transport governed by the convection-diffusion-reaction (CDR) equation in 2D flow. The efficiency of solving computationally partial differential equations can be illustrated by using a precise numerical method that yields remarkable precision at a low cost. The accuracy and computational efficiency of two second-order finite difference methods were investigated. The results were compared to a finite volume technique, which has a memory advantage and conserves mass, momentum, and energy even on coarse grids. For various diffusion coefficient values, numerical simulation of unsteady CDR equation are also performed. The techniques were examined for consistency and convergence. The effectiveness and accuracy of these approaches for solving CDR equations are demonstrated by simulation results. Efficiency is measured using L2 and L∞, and the estimated results are compared to the corresponding analytical solution.
format Article
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institution Kabale University
issn 1687-9651
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series International Journal of Differential Equations
spelling doaj-art-ec1b428355344d279edbc44173615b3f2025-02-03T05:53:50ZengWileyInternational Journal of Differential Equations1687-96512022-01-01202210.1155/2022/3476309Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small ParametersUzair Ahmed0Daoud Suleiman Mashat1Dalal Adnan Maturi2Department of MathematicsDepartment of MathematicsDepartment of MathematicsConvection, diffusion, and reaction mechanisms are characteristics of transient mass-transfer phenomena that occur in natural and industrial systems. In this article, we contemplate a passive scalar transport governed by the convection-diffusion-reaction (CDR) equation in 2D flow. The efficiency of solving computationally partial differential equations can be illustrated by using a precise numerical method that yields remarkable precision at a low cost. The accuracy and computational efficiency of two second-order finite difference methods were investigated. The results were compared to a finite volume technique, which has a memory advantage and conserves mass, momentum, and energy even on coarse grids. For various diffusion coefficient values, numerical simulation of unsteady CDR equation are also performed. The techniques were examined for consistency and convergence. The effectiveness and accuracy of these approaches for solving CDR equations are demonstrated by simulation results. Efficiency is measured using L2 and L∞, and the estimated results are compared to the corresponding analytical solution.http://dx.doi.org/10.1155/2022/3476309
spellingShingle Uzair Ahmed
Daoud Suleiman Mashat
Dalal Adnan Maturi
Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
International Journal of Differential Equations
title Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
title_full Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
title_fullStr Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
title_full_unstemmed Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
title_short Finite Volume Method for a Time-Dependent Convection-Diffusion-Reaction Equation with Small Parameters
title_sort finite volume method for a time dependent convection diffusion reaction equation with small parameters
url http://dx.doi.org/10.1155/2022/3476309
work_keys_str_mv AT uzairahmed finitevolumemethodforatimedependentconvectiondiffusionreactionequationwithsmallparameters
AT daoudsuleimanmashat finitevolumemethodforatimedependentconvectiondiffusionreactionequationwithsmallparameters
AT dalaladnanmaturi finitevolumemethodforatimedependentconvectiondiffusionreactionequationwithsmallparameters