Fast Modeling of Radiation and Conduction Heat Transfer and application example

The release of CUDA by NVIDIA in 2007 has tremendously increased GPU programmability, thus allowing scientific and engineering applications to take advantage of the high GPU compute capability. In this work, we present ultra-fast solutions for radiation and diffusion heat transfer on the GPU. First, the Multiple Absorption Coefficient Zonal Method (MACZM) for computing direct radiative exchange factors in 3D semi-transparent media is reviewed and validated. Then, an efficient implementation of MACZM is presented, based on discrete geometry algorithms, and an optimized GPU CUDA parallelization. The CUDA implementation achieves 300 to 600 times speed-up. The Non-recursive Plating Algorithm (NRPA), a non-recursive version of the plating algorithm for computing total exchange factors is then formulated. Due to low-complexity matrix multiplication algorithms, the NRPA has lower complexity than the PA does and it runs up to 750 times faster on the GPU by comparison to the CPU PA. On the other hand, an efficient GPU implementation for the Locally One Dimensional (LOD) finite difference split method for solving heat diffusion is presented, based on an optimized alternation between parallelization schemes and equation solvers, achieving accelerations from 75 to 250 times. Finally, all the methods are applied together for solving 3D heat transfers in a steel reheating furnace. A multi-grid approach is applied for MACZM and a zone-by-zone computation for the NRPA. As a result, high precision and very fast computation time are achieved, making the methods of high interest for building precise and efficient control units. (author)