Improving radiative transfer accuracy in complex shapes with UCWQ

Abstract

Accurate representation of coordinates and the computation of the angular quadrature coefficients μ, ξ, and η in complex geometries are essential for advancing the understanding of astrophysical phenomena and various industrial applications. This paper builds upon prior work titled " Enhanced discrete ordinates approach for mitigating shadowing effects in obstructed gas-filled spaces: Implications for astrophysical and industrial applications", which introduced Uniform Constant Weight Quadrature (UCWQ) to address challenges associated with the discrete ordinates method (DOM). Specifically, this research tackles issues related to computational inefficiency and accuracy loss in complex radiative transfer scenarios. The innovative Pyramidal Angular Mesh (PAM) exhibits an R-squared value of 0.9965. This high statistical agreement directly translates to increased reliability and underscores the model's strengths in accurately simulating radiative heat transfer, particularly in complex geometrical configurations. A comparative analysis highlights UCWQ's superior performance with its PAM design over other quadrature methods, such as S_N and T_N, as well as the Finite Volume Method (FVM). Unique aspects of UCWQ include the unlimited choice of directions afforded by the PAM design. This versatile technique is valuable for studying astrophysical systems and analyzing the radiative effects of greenhouse gases, particularly concerning shadowing and ray effects and obstructions in industrial furnaces.•Employing a novel Pyramidal Angular Mesh (PAM) design to advance the analysis of complex geometries.•A head-to-head comparison of UCWQ and FVM in terms of performance and accuracy.•Presenting comprehensive findings and error metrics to assess performance improvements and validate the method.