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A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity

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

A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity Thumbnail


Authors

Mofdi El-Amrani

Anouar Obbadi

Driss Yakoubi



Abstract

A fractional-step method is proposed and analyzed for solving the incompressible thermal Navier–Stokes equations coupled to the convection–conduction equation for heat transfer with a generalized source term for which the viscosity and thermal conductivity are temperature-dependent under the Boussinesq assumption. The proposed method consists of four steps all based on a viscosity-splitting algorithm where the convection and diffusion terms of both velocity and temperature solutions are separated while a viscosity term is kept in the correction step at all times. This procedure preserves the original boundary conditions on the corrected velocity and it removes any pressure inconsistencies. As a main feature, our method allows the temperature to be transported by a non-divergence-free velocity, in which case we show how 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. The theoretical results are examined by an accuracy test example with known analytical solution and using a benchmark problem of Rayleigh–Bénard convection with temperature-dependent viscosity and thermal conductivity. We also apply the method for solving a problem of unsteady flow over a heated airfoil. The obtained results demonstrate the convergence, accuracy and applicability of the proposed time viscosity-splitting method.

Citation

El-Amrani, M., Obbadi, A., Seaid, M., & Yakoubi, D. (2024). A time viscosity-splitting method for incompressible flows with temperature-dependent viscosity and thermal conductivity. Computer Methods in Applied Mechanics and Engineering, 429, Article 117103. https://doi.org/10.1016/j.cma.2024.117103

Journal Article Type Article
Acceptance Date May 27, 2024
Online Publication Date Jun 12, 2024
Publication Date Sep 1, 2024
Deposit Date Jul 12, 2024
Publicly Available Date Oct 30, 2024
Journal Computer Methods in Applied Mechanics and Engineering
Print ISSN 0045-7825
Electronic ISSN 1879-2138
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 429
Article Number 117103
DOI https://doi.org/10.1016/j.cma.2024.117103
Public URL https://durham-repository.worktribe.com/output/2493126

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