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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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2022/3476309 |
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| _version_ | 1832553508435394560 |
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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 |
| id | doaj-art-ec1b428355344d279edbc44173615b3f |
| 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 |