Monte Carlo Ray Tracing (MCRT) is one common technique to characterize radiation exchange between surfaces. One MCRT algorithm approach considers the probability of each reflection, with non-reflected rays terminating (Forward MCRT). Here, the fraction of rays that are reflected are associated with the absorptivity of the surface. This approach generally requires a large ray count to provide a sufficient number of rays that survive multiple reflection events. In this work, we explore efficient MCRT approaches and pose additional computational methods that improve modeling efficiency to predict the apparent behavior of cavities. These efficient MCRT approaches include: uniformly distributed ray origins, use of the power absorption scheme, use of a Ray Count Power Series (RCPS), utilizing diffuse emission, and exploiting symmetry and boundary conditions.

Numerous ray origins for MCRT are required to adequately represent and span the origin surface. However, random assignment of these origins leads to long convergence times and significant computational effort to avoid clusters or voids of ray origins on an emitting surface. We show the use of distributed grids of emission points that avoid locally dense or sparse origins to reduce convergence time while providing low computational error. In particular, the introduction of a Ray Count Power Series (RCPS) in this work allows any intrinsic emissivity/absorptivity to be applied to the cavity interior surfaces in post-processing to obtain the apparent emissivity/absorptivity. The RCPS records the cumulative count of rays that experience a certain number of reflections within the cavity and is used to determine the apparent cavity emission/absorption for any intrinsic property using a single MCRT calculation. An alternative MCRT approach using a power absorption scheme that tracks the reduction of the radiative energy of each ray (as governed by the absorptivity of the surface) requires a lower ray count than traditional approaches as each ray is tracked through its entire path until the ray no longer interacts with the surfaces or cavity. The significance of simplifications such as symmetry and periodic boundary conditions on the number of traced rays is discussed. Finally, we show that Kirchhoff's Law also applies for apparent surfaces representing cavity openings, enabling the determination of radiative properties by equivalence. Methods provided in this work can be used to improve computational efficiency in MCRT modeling approaches with specific applications in apparent cavity behavior.