Analysis of stability, energy conservation, and convergence of coupled advection-diffusion models for ocean-atmosphere interactions

Taj Munir, Hongchu Chen, Can Kang and Hussan Zeb

Applied Mathematics and Computation, 2025, vol. 502, issue C

Abstract: The main focus of this work is to study ocean-atmosphere coupling, modeled using coupled advection-diffusion equations with two coupling conditions: the Dirichlet-Neumann (DN) and the heat flux condition, defined across two non-overlapping domains. For numerical approximation, the finite-volume method (FVM) and finite-difference method (FDM) are applied. The convergence analysis of the coupled problem is conducted using the Generalized Minimal Residual (GMRES) method. We conclude that central difference schemes ensure conservation under heat flux coupling, while one-sided differences introduce errors leading to energy non-conservation. While for the DN-coupling one sided maintain the conservation. The stability analysis, based on Fourier analysis and normal mode techniques from Godunov-Ryabenkii (GR) stability theory, reveals stricter stability constraints for explicit schemes compared to implicit ones. The GMRES method is used to achieve numerical convergence. The results demonstrate how variations in the Péclet number (Pe) influence the behavior of the solution, transitioning from diffusion-driven smoothness to advection-driven sharpness, while maintaining physical consistency across the domains. The proposed algorithms undergo rigorous numerical validation, with results illustrated through detailed graphs and numerical tables that demonstrate strong agreement between theoretical predictions and computational outcomes.

Keywords: Advection-diffusion (AD) equations; Finite volume and difference schemes; Discrete mass/energy conservation; Heat flux coupling; DN-coupling; Stability analysis and ocean-atmosphere coupling (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032500222X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:502:y:2025:i:c:s009630032500222x

DOI: 10.1016/j.amc.2025.129496

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().