Macro-voxel algorithm for adaptive grid generation to accelerate grid traversal in the radiative heat transfer analysis via Monte Carlo method

In the thermal radiation analysis via Monte Carlo method, the ray tracing algorithm often consumes a significant fraction of CPU time. As such, an efficient grid traversal algorithm can considerably affect the performance of the Monte Carlo method. This paper presents a new grid traversal acceleration algorithm by merging adjacent small empty voxels in a preprocessing step due to the fact that larger empty space, named “macro-voxel”, allows for traversing a ray over a large distance at a smaller cost. The proposed algorithm is validated theoretically, and the results are examined for a gray box with diffuse surfaces. Timing results of the new algorithm are compared with the USD method in a typical 3D radiation furnace with concave geometry and the speedup ratio of both the macro-voxel algorithm and the USD method with respect to direct method are calculated for an optimal grid of voxels. For the considered geometry, the macro-voxel algorithm is found to be clearly superior to the USD even if the size of the problem is large and the geometry is not convex.