Parallel algorithm and its convergence of spatial domain decomposition of discrete ordinates method for solving radiation heat transfer problem

To improve the computational efficiency and hold calculation accuracy at the same time, we study the parallel computation for radiation heat transfer. In this paper, the discrete ordinates method (DOM) and the spatial domain decomposition parallelization (DDP) are combined by message passing interface (MPI) language. The DDP–DOM computation of the radiation heat transfer within the rectangular furnace is described. When the result of DDP–DOM along one-dimensional direction is compared with that along multi-dimensional directions, it is found that the result of the latter one has higher precision without considering the medium scattering. Meanwhile, an in-depth study of the convergence of DDP–DOM for radiation heat transfer is made. Analyzing the cause of the weak convergence, we relate the total number of iteration steps when the convergence is obtained to the number of sub-domains. When we decompose the spatial domain along one-, two- and three-dimensional directions, different linear relationships between the number of total iteration steps and the number of sub-domains will be possessed separately, then several equations are developed to show the relationships. Using the equations, some phenomena in DDP–DOM can be made clear easily. At the same time, the correctness of the equations is verified.