A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids

El-Amrani, Mofdi; Obbadi, Anouar; Seaid, Mohammed; Yakoubi, Driss

Abstract

We propose a fractional-step method for the numerical solution of unsteady thermal convection in non-Newtonian fluids with temperature-dependent physical parameters. The proposed method is based on a viscosity-splitting approach, and it consists of four uncoupled steps where the convection and diffusion terms of both velocity and temperature solutions are uncoupled while a viscosity term is kept in the correction step at all times. This fractional-step method maintains the same boundary conditions imposed in the original problem for the corrected velocity solution, and it eliminates all inconsistencies related to boundary conditions for the treatment of the pressure solution. In addition, the method is unconditionally stable, and it allows the temperature to be transported by a non-divergence-free velocity field. In this case, we introduce a methodology to handle the subtle temperature convection term in the error analysis and establish full first-order error estimates for the velocity and the temperature solutions and 1/2-order estimates for the pressure solution in their appropriate norms. Three numerical examples are presented to demonstrate the theoretical results and examine the performance of the proposed method for solving unsteady thermal convection in non-Newtonian fluids. The computational results obtained for the considered examples confirm the convergence, accuracy, and applicability of the proposed time fractional-step method for unsteady thermal convection in non-Newtonian fluids.

Citation

El-Amrani, M., Obbadi, A., Seaid, M., & Yakoubi, D. (2025). A fractional time-stepping method for unsteady thermal convection in non-Newtonian fluids. Communications in Nonlinear Science and Numerical Simulation, 140, Article 108350. https://doi.org/10.1016/j.cnsns.2024.108350

• Journal Article Type: Article
• Acceptance Date: Sep 12, 2024
• Online Publication Date: Sep 18, 2024
• Publication Date: 2025-01
• Deposit Date: Oct 4, 2024
• Publicly Available Date: Oct 30, 2024
• Journal: Communications in Nonlinear Science and Numerical Simulation
• Print ISSN: 1007-5704
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 140
• Article Number: 108350
• DOI: https://doi.org/10.1016/j.cnsns.2024.108350
• Public URL: https://durham-repository.worktribe.com/output/2873113