Fast kd‐tree‐based hierarchical radiosity for radiative heat transport problems

In this paper we present a new efficient approach for radiative heat transfer simulations for various applications in engineering, combining existing approaches from different fields of computer science and heat transfer. For these application fields we assume radiative exchange between gray, diffuse surfaces in a radiatively nonparticipating medium. To solve the complex space–time behavior of radiation in 3D domains we use the hierarchical radiosity method. Here, the basic idea is to hierarchically subdivide surfaces forming a quad‐tree structure until a refinement criterion is reached. The fundamental underlying operation of the radiosity method is visibility detection which can be solved efficiently by using a space partitioning approach for the input surfaces. For this reason we choose a kd‐tree which is the best known acceleration structure for visibility detection on irregularly distributed surfaces. These approaches dramatically decrease the complexity of the radiation problem from n³ to O((k² + n)logk), where k is the number of input surfaces and n is the number of refined surfaces. We validate the approach for several non‐trivial examples and demonstrate that the scheme is second‐order accurate. Copyright © 2011 John Wiley & Sons, Ltd.