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Anderson acceleration in the finite volume method for non-Newtonian convective flows with thermal coupling.

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Title: Anderson acceleration in the finite volume method for non-Newtonian convective flows with thermal coupling.
Authors: Díaz, Felipe A.1 (AUTHOR) felipe.diaz.mo@usach.cl, Castillo, E.1 (AUTHOR) ernesto.castillode@usach.cl, Cabrales, Roberto Carlos2 (AUTHOR) roberto.cabrales@gmail.com, Moraga, N.O.3 (AUTHOR) nmoraga@userena.cl, Aguirre, Ismael4 (AUTHOR) ismael.aguirre@usach.cl
Source: International Journal of Numerical Methods for Heat & Fluid Flow. 2026, Vol. 36 Issue 7, p2628-2648. 21p.
Subjects: Finite volume method, Non-Newtonian flow (Fluid dynamics), Iterative methods (Mathematics), Convective flow, Viscosity, Computational fluid dynamics
Abstract: Purpose: This study aims to evaluate the Anderson acceleration (AA) method as a strategy to improve convergence efficiency in thermally coupled, convection-dominated non-Newtonian flows with temperature-dependent properties. Although AA has proven effective in accelerating iterative methods in other computational contexts, its application to fluid flow and heat transfer problems with variable thermophysical properties has not yet been systematically assessed. These systems are particularly challenging, as the interaction between non-Newtonian rheology and thermal feedback introduces strong nonlinearities that make them difficult to solve using traditional iterative methods. Design/methodology/approach: To assess the benefits of AA, the method was implemented by an in-house finite volume code and tested on benchmark natural convection problems. Both Newtonian and pseudoplastic fluids with temperature-dependent viscosity were analyzed to capture the influence of rheology on thermally coupled flow behavior. Convergence performance was evaluated in terms of the number of iterations required for both steady and transient regimes and compared directly with the standard Picard fixed-point approach. Findings: The results show that AA preserves the accuracy of the reference solutions while substantially reducing the number of iterations required for convergence. For steady problems, the iteration count decreased by up to 11.3 times, while in transient cases the savings reached up to 2.2 times for Newtonian fluids and 2.4 times for pseudoplastic cases. These improvements result in a significant reduction in computational effort for thermally coupled non-Newtonian flows. Originality/value: This work introduces AA as a practical, reliable and efficient technique for simulating thermally coupled non-Newtonian flows with temperature-dependent properties within a finite volume framework. Beyond demonstrating its effectiveness in this challenging class of problems, this study suggests that the present formulation could serve as a foundation for extending AA to more complex multiphysics scenarios, such as multiphase or solid–liquid phase-change systems. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Purpose: This study aims to evaluate the Anderson acceleration (AA) method as a strategy to improve convergence efficiency in thermally coupled, convection-dominated non-Newtonian flows with temperature-dependent properties. Although AA has proven effective in accelerating iterative methods in other computational contexts, its application to fluid flow and heat transfer problems with variable thermophysical properties has not yet been systematically assessed. These systems are particularly challenging, as the interaction between non-Newtonian rheology and thermal feedback introduces strong nonlinearities that make them difficult to solve using traditional iterative methods. Design/methodology/approach: To assess the benefits of AA, the method was implemented by an in-house finite volume code and tested on benchmark natural convection problems. Both Newtonian and pseudoplastic fluids with temperature-dependent viscosity were analyzed to capture the influence of rheology on thermally coupled flow behavior. Convergence performance was evaluated in terms of the number of iterations required for both steady and transient regimes and compared directly with the standard Picard fixed-point approach. Findings: The results show that AA preserves the accuracy of the reference solutions while substantially reducing the number of iterations required for convergence. For steady problems, the iteration count decreased by up to 11.3 times, while in transient cases the savings reached up to 2.2 times for Newtonian fluids and 2.4 times for pseudoplastic cases. These improvements result in a significant reduction in computational effort for thermally coupled non-Newtonian flows. Originality/value: This work introduces AA as a practical, reliable and efficient technique for simulating thermally coupled non-Newtonian flows with temperature-dependent properties within a finite volume framework. Beyond demonstrating its effectiveness in this challenging class of problems, this study suggests that the present formulation could serve as a foundation for extending AA to more complex multiphysics scenarios, such as multiphase or solid–liquid phase-change systems. [ABSTRACT FROM AUTHOR]
ISSN:09615539