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# Methods to Accelerate Ray Tracing in the Monte Carlo Method for Surface-to-Surface Radiation Transport

[+] Author and Article Information
Sandip Mazumder

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43202mazumder.2@osu.edu

J. Heat Transfer 128(9), 945-952 (Feb 09, 2006) (8 pages) doi:10.1115/1.2241978 History: Received November 15, 2005; Revised February 09, 2006

## Abstract

Two different algorithms to accelerate ray tracing in surface-to-surface radiation Monte Carlo calculations are investigated. The first algorithm is the well-known binary spatial partitioning (BSP) algorithm, which recursively bisects the computational domain into a set of hierarchically linked boxes that are then made use of to narrow down the number of ray-surface intersection calculations. The second algorithm is the volume-by-volume advancement (VVA) algorithm. This algorithm is new and employs the volumetric mesh to advance the ray through the computational domain until a legitimate intersection point is found. The algorithms are tested for two classical problems, namely an open box, and a box in a box, in both two-dimensional (2D) and three-dimensional (3D) geometries with various mesh sizes. Both algorithms are found to result in orders of magnitude gains in computational efficiency over direct calculations that do not employ any acceleration strategy. For three-dimensional geometries, the VVA algorithm is found to be clearly superior to BSP, particularly for cases with obstructions within the computational domain. For two-dimensional geometries, the VVA algorithm is found to be superior to the BSP algorithm only when obstructions are present and are densely packed.

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## Figures

Figure 1

Schematic representation of the bisection scheme in the BSP algorithm, the definition of “level,” and the unique numbering pattern of the various boxes (or leaves)

Figure 2

Illustration of water tightness: In this example, if a ray-box intersection is performed with the bounding box of Child 2, an intersection is not found. This would suggest that the ray must hit something that belongs to Child 1. If the shared face belongs to Child 2 alone, the ray will never find an intersection and will escape though an artificially created hole.

Figure 3

Illustration of recursion in the BSP algorithm, showing that any scenario a child faces is what its mother has already encountered before, thereby allowing recursive procedures

Figure 4

An example illustrating the working mechanism of the BSP algorithm: (a) The geometry, the emitted ray, and the various boxes in its path, (b) the boxes and sub-boxes for which the search flag becomes 1 are shaded gray

Figure 5

Comparison of Monte Carlo results with results obtained using the view-factor method: The statistical errors were computed using 9 ensembles, and the error bars shown correspond to ± std. dev. The statistical errors for 106 rays are so small that they are not visible on the plots.

Figure 6

Geometry used for the test cases considered in the present study

Figure 7

Performance characteristics of the VVA algorithm in 3D geometries, and the scaling laws derived from them

Figure 8

Performance characteristics of the BSP algorithm in 3D geometries, and the scaling laws derived from them

## Errata

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