Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media

Salhi, Loubna; Seaid, Mohammed; Yakoubi, Driss

Abstract

We present an iterative scheme for the numerical analysis of propagating reaction front problems in porous media satisfying an Arrhenius-type law. The governing equations consist of the Darcy equations for the pressure and flow field coupled to two convection–diffusion–reaction equations for the temperature and depth of conversion. Well-posedness, existence and uniqueness of the weak solution are first studied using a fixed-point approach and then, analysis of the proposed iterative scheme is investigated. Numerical results are also presented in order to validate the theoretical estimates and to illustrate the performance of the proposed scheme. The obtained results are in line with our expectations for a good numerical resolution with high accuracy and stability behaviors.

Citation

Salhi, L., Seaid, M., & Yakoubi, D. (2024). Convergence analysis of a class of iterative methods for propagation of reaction fronts in porous media. Computer Methods in Applied Mechanics and Engineering, 418(Part A), Article 116524. https://doi.org/10.1016/j.cma.2023.116524

• Journal Article Type: Article
• Acceptance Date: Oct 6, 2023
• Online Publication Date: Oct 11, 2023
• Publication Date: Jan 1, 2024
• Deposit Date: Nov 9, 2023
• Publicly Available Date: Nov 14, 2023
• Journal: Computer Methods in Applied Mechanics and Engineering
• Print ISSN: 0045-7825
• Electronic ISSN: 1879-2138
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 418
• Issue: Part A
• Article Number: 116524
• DOI: https://doi.org/10.1016/j.cma.2023.116524
• Public URL: https://durham-repository.worktribe.com/output/1903545