Evaluation of numerical accuracy in CFD simulations of natural convection via Grid Convergence Index using OpenFOAM

Abstract

Natural convection heat transfer is a highly relevant phenomenon, frequently analyzed through Computational Fluid Dynamics (CFD) simulations. However, the accuracy of these simulations depends directly on the quality of the numerical mesh. In this context, the importance of mesh convergence studies becomes clear as an essential step to ensure reliability and reduce uncertainties associated with spatial discretization. This article aims to perform a mesh convergence analysis for a three-dimensional numerical simulation of natural convection on a flat plate, using CFD through the open-source software OpenFOAM. The methodology consisted of applying the Grid Convergence Index (GCI), recommended by ASME, employing three meshes with different levels of refinement and an inflation layer to solve the thermal boundary layer. The heat flux on the plate surface was adopted as the variable of interest. The numerical results obtained were compared with consolidated values of empirical correlations for the Nusselt number. The results showed that mesh refinement significantly impacts the heat flux values, with the most refined mesh presenting an error of only 2.21% compared to the empirical correlation. Quantitative analysis via GCI indicated consistent values ​​above 5% for most mesh pairs, confirming the sensitivity of the solution to discretization. However, the intermediate mesh, with seven prism layers, presented the best balance between accuracy and computational cost, making it the most recommended for practical applications. It is concluded that mesh convergence studies are a crucial step in ensuring the reliability of CFD simulations.