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Consistency and Stability Analysis of a Mathematical Model of Chlorine Concentration in Contact Tanks Using Numerical Solution of a 1- Dimensional Convection-Diffusion Equation
Subject area: Science,Engineering and Technology · Area of research: Applied Mathematics
Abstract
In this paper we consider the consistency and stability analysis of the modified convection diffusion equation: which describes the mass transfer of chlorine in contact tank water disinfectant. We employ the concept of Dufort-Frankel based on Richardson?s scheme to discretize the modified equation. This resulted to a numerical scheme algorithm. The consistency was analyzed by Taylor?s expansion of the discretized scheme, which was found to be consistent with the original modified equation. In addition, stability was analyzed by using matrix method. The numerical computation results showed that the scheme was conditionally stable. This has been concluded by numerical computations to illustrate the consistence and stability of the scheme.
Keywords
Consistency analysis ,Coupled convection-diffusion equation, discretized schemes, stability analysis.
References
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[2] Du-Fort E.C. and Frankel S.P., (1953): Stability conditions in the numerical treatment of parabolic differencial equations. [Available online at https: www.jstor.org].
[3] Ishaq M.S, Afsheen Z, Khan A. and Khan A., (2018): Disinfection Methods. [Available online at https://www.intechopen.com].
[4] Mudde R.F. and Akker V.D., (1991): Transport Phenomena: The Art of Balancing 1st Edition-Amazon.com. [Available online at https://www.amazon.com].
[5] Oram B., (2021): Chlorine Disinfection Contact Time (Basic)-Water-Research.net. [Available online at https://www.knowyourh2o.com].
[6] Villanueva C.M., Cordier S., Ribera L.F., Salas L.A., (2015): Overview of Disinfection By-products and Associated Health Effects. [Available online at https://www.researchgate.net].
[7] Zhao.Q.L. and Zhang.Y.Z., (2017). Concentration distribution of chloride ion under the influence of the convection-diffusion coupling. Hindawi Advances in Materials Science and Engeneering. doi.org/10.1155/2017/2076986.
How to cite this paper
@article{1703149,
author = {Owuor Lucas Otieno, Boniface O. Kwach, Frankline Tireito, Linda Ouma},
title = {Consistency and Stability Analysis of a Mathematical Model of Chlorine Concentration in Contact Tanks Using Numerical Solution of a 1- Dimensional Convection-Diffusion Equation},
journal = {Iconic Research And Engineering Journals},
year = {2022},
volume = {5},
number = {7},
pages = {257-261},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/17031491.pdf},
abstract = {In this paper we consider the consistency and stability analysis of the modified convection diffusion equation: which describes the mass transfer of chlorine in contact tank water disinfectant. We employ the concept of Dufort-Frankel based on Richardson?s scheme to discretize the modified equation. This resulted to a numerical scheme algorithm. The consistency was analyzed by Taylor?s expansion of the discretized scheme, which was found to be consistent with the original modified equation. In addition, stability was analyzed by using matrix method. The numerical computation results showed that the scheme was conditionally stable. This has been concluded by numerical computations to illustrate the consistence and stability of the scheme.},
keywords = {Consistency analysis ,Coupled convection-diffusion equation, discretized schemes, stability analysis.},
month = {January},
}