Development and performance evaluation of fully coupled finite volume solvers using Newton iteration for mixed convection flow problems

Behnam Cheraghi, Shidvash Vakilipour, Masoud Mohammadi and Rasoul Rahmati

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 241, issue PA, 134-170

Abstract: This study presents the development and performance evaluation of fully coupled finite volume solvers employing Newton iteration for solving mixed convection flow problems. The coupled solvers introduced by Vakilipour and Ormiston (2012) and Mohammadi et al. (2021) are extended to three dimensions within the foam-extend framework (foam-extend Project, 2013). Implementing Newton Linearization of discretized governing equations, four coupled solvers are developed: Coupled Picard Linearization (CPL), Coupled Newton Linearization for Energy equation (CNLE), Coupled Newton Linearization for Momentum equation (CNLM), and Coupled Newton Linearization for Energy and Momentum equations (CNLEM). A spectrum of two and three-dimensional benchmark mixed convection flow cases is chosen to evaluate the computational performance of developed coupled solvers. The solvers are designed to address the numerical challenges arising in high Reynolds and Richardson flow regimes, where the solution convergence is either too low or not achievable with the Picard iteration. The variable time stepping technique is used to mitigate solution instabilities and to expedite its convergence during early and later stages of the solution iterations, respectively. Four developed coupled solvers are compared and it is demonstrated that CNLEM outperforms the others, particularly in scenarios with strong nonlinearities. The solver’s ability to handle both momentum and buoyancy-dominated flows makes it versatile for a wide range of applications. Moreover, the CNLEM solver is shown to be particularly effective in handling complex flow scenarios with high nonlinearities, offering significant improvements in computational efficiency.

Keywords: Newton iteration; Fully coupled solver; Finite volume method; Mixed convection flow; Foam-extend (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:241:y:2026:i:pa:p:134-170

DOI: 10.1016/j.matcom.2025.08.019

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