Quantitative evaluation of the computational accuracy for the Monte Carlo calculation of radiative heat transfer

Generally, there is no common method for directly and quantitatively evaluating computational errors in the calculation of radiative transfer. A method for quantitatively evaluating the accuracy in calculation of radiative transfer using the Monte Carlo method (MCM) is proposed, which is based on setting a radiative transfer enclosure in an isothermal and radiative equilibrium state, i.e. a state that equates exactly to a blackbody. For a gray emitting, absorbing, isotropically scattering, cubic enclosure bounded with diffusely emitting and reflecting surfaces, the computational accuracy and efficiency of the MCM are examined under fixed, constant surface emissivity of 0.5 and medium scattering albedo of 0.5. The concept of Mean Optical Thickness per Element (MOTE), that is the product of the absorption coefficient and the average length of three coordinate directions of the discrete space elements, is proposed to serve as a key scaling parameter to evaluate the calculation errors. When the MOTE is less than around 0.1, the errors for the surface elements reach a minimum level, even if the mesh density continues to increase. Scaling laws have been set up to relate the minimum errors for both the surface elements and space elements with the variation in the number of energy bundles (NEB). A desirable calculation error level is set as 1.0% for radiative heat transfer with an acceptable cost, for which the minimum NEBs are 3000 and 750 for the surface and space elements, respectively. For the surface elements, a scaling law relating the NEB and the maximum MOTE has been obtained that will enable the desirable error not to be exceeded; for the space elements, achieving the desirable error is dominated by the NEB, not the MOTE. It is stated that the cases studied in the paper have many limitations, and additional research should be done in the future to address the real cases of interest.