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An iterative scheme for solving a coupled Darcy–convection–diffusion model

El-Amrani, Mofdi; Salhi, Loubna; Seaid, Mohammed; Yakoubi, Driss

An iterative scheme for solving a coupled Darcy–convection–diffusion model Thumbnail


Authors

Mofdi El-Amrani

Loubna Salhi

Driss Yakoubi



Abstract

We present an iterative scheme for the numerical analysis of a class of coupled Darcy-convection-diffusion problems modelling flow and heat transfer in porous media. The governing equations consist of the Darcy equations for the flow coupled to a convection-diffusion equation for heat transfer with nonlinear viscosity and diffusion coefficient depending on the temperature. Existence and uniqueness of the weak solution for the considered problem are first analyzed using a fixed-point method and then convergence study of two iterative schemes for the fixed-point algorithm is presented. Two numerical examples are selected to validate the theoretical estimates and to demonstrate the performance of the proposed algorithm. The obtained results support our theoretical expectations for a good numerical convergence with the developed estimates.

Citation

El-Amrani, M., Salhi, L., Seaid, M., & Yakoubi, D. (2023). An iterative scheme for solving a coupled Darcy–convection–diffusion model. Journal of Mathematical Analysis and Applications, 517(2), Article 126603. https://doi.org/10.1016/j.jmaa.2022.126603

Journal Article Type Article
Acceptance Date Aug 10, 2022
Online Publication Date Aug 24, 2022
Publication Date Jan 15, 2023
Deposit Date Apr 5, 2023
Publicly Available Date Oct 30, 2024
Journal Journal of Mathematical Analysis and Applications
Print ISSN 0022-247X
Electronic ISSN 1096-0813
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 517
Issue 2
Article Number 126603
DOI https://doi.org/10.1016/j.jmaa.2022.126603
Public URL https://durham-repository.worktribe.com/output/1177641

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