A Submesh Finite Element Method for the Calculation of View Factor

The finite element method (FEM) for view factor calculation is prone to singularities due to the negative power of distance in the integrand. To address this issue, this study proposes a submesh FEM based on triangular mesh subdivision. Two submesh generation methods are developed using the nodes and integral points of triangular elements. The accuracy of the proposed method is validated through two benchmark cases, namely the view factor calculation of two perpendicular unit squares sharing a common edge and the radiative heat transfer in a typical radiant heating room. Parametric studies reveal that the computational performance is simultaneously affected by the submesh generation method, the integration order combination, and the number of subdivision cycles. The proposed method achieves high accuracy in both benchmarks, with a relative error as low as 0.0049% for the view factor calculation and a maximum relative error of 1.04% for the radiative heat transfer rate. The results demonstrate that the proposed submesh FEM effectively resolves the singularity issue of the conventional FEM for view factor calculations in radiative heat transfer.