Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 20 August 2021
Issue publication date: 19 April 2022
Abstract
Purpose
The purpose of this paper is to describe an extension of the boundary element method (BEM) and the dual reciprocity boundary element method (DRBEM) formulations developed for one- and two-dimensional steady-state problems, to analyse transient convection–diffusion problems associated with first-order chemical reaction.
Design/methodology/approach
The mathematical modelling has used a dual reciprocity approximation to transform the domain integrals arising in the transient equation into equivalent boundary integrals. The integral representation formula for the corresponding problem is obtained from the Green’s second identity, using the fundamental solution of the corresponding steady-state equation with constant coefficients. The finite difference method is used to simulate the time evolution procedure for solving the resulting system of equations. Three different radial basis functions have been successfully implemented to increase the accuracy of the solution and improving the rate of convergence.
Findings
The numerical results obtained demonstrate the excellent agreement with the analytical solutions to establish the validity of the proposed approach and to confirm its efficiency.
Originality/value
Finally, the proposed BEM and DRBEM numerical solutions have not displayed any artificial diffusion, oscillatory behaviour or damping of the wave front, as appears in other different numerical methods.
Keywords
Acknowledgements
The authors would express their acknowledgement and gratitude to the referees and the editor for their suggestions, comments and recommendations which improved the final version of this paper. The first author would also like to thank the Ministry of Higher Education and Scientific Research of Iraq and Al-Nahrain University for supporting this research work.Conflict of interests: This research paper is purely academic, and no potential conflict of interests is found related to the publication of this paper.
Citation
Al-Bayati, S.A. and Wrobel, L.C. (2022), "Numerical modelling of convection-diffusion problems with first-order chemical reaction using the dual reciprocity boundary element method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 5, pp. 1793-1823. https://doi.org/10.1108/HFF-12-2020-0789
Publisher
:Emerald Publishing Limited
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