An optimized and accurate Monte Carlo method to simulate 3D complex radiative enclosures

The modeling of radiative heat transfer in complex radiant enclosures is a particularly challenging subject. This simulation is often best treated by calculating distribution factors through the Monte Carlo method. In order to enhance performance of the Monte Carlo method, efficient algorithms to find location of emission and direction of emission in the original Monte Carlo method are implemented. Next, the best ray tracing algorithm is introduced by comparing timing results of the USD, the BSP, the Simplex and the VVA acceleration ray tracing algorithms to make it numerically efficient as possible. Also, the constrained maximum likelihood estimation is used to enhance accuracy of the Monte Carlo by smoothing inherent random errors in the estimated distribution factors to simultaneously satisfy both of the reciprocity and summation rules. Accuracy of the Monte Carlo method is tested for a classical problem, namely a 3D box, with diffuse gray walls. For efficiency study, the optimized Monte Carlo method is then tested for two real radiative enclosures with convex and concave geometries. All ray tracing algorithms are found to result in computational gains, with respect to direct calculations that do not employ any acceleration technique. In the considered test cases, the VVA and the USD algorithms are found to be clearly superior to the BSP and the Simplex algorithms, particularly for concave geometries that have some obstructions within the computational domain.