An Enhanced Hybrid Methodology for Iteration Error Estimation and Reduction in Heat Transfer Modeling

Abstract

In the realm of numerical simulations for heat transfer problems, the precision of iterative solutions is paramount. This study introduces an innovative hybrid methodology designed to refine iteration error estimation and ameliorate the accuracy of numerical solutions in heat transfer models encompassing diffusion and advection phenomena. Central to this methodology is the development of a novel estimator, predicated on the rate of iterative convergence. The efficacy and versatility of the proposed estimator and the overarching hybrid approach are scrutinized through the analysis of two distinct one-dimensional and a singular two-dimensional heat transfer model. In these applications, it has been demonstrated that the application of the refined methodology significantly enhances the precision of iteration error estimates, particularly in the initial phases of iteration. This improvement in accuracy and reliability of iteration error estimates was consistently observed across all examined models and pertinent variables. Notably, the incorporation of this methodology into existing simulation frameworks is straightforward, marking a substantial advancement in the domain of iteration error estimation. The findings underscore the utility of the proposed hybrid approach in achieving more precise and reliable numerical solutions in a wide array of heat transfer models, thereby contributing to the fidelity and robustness of computational simulations in thermal engineering.