A parallel algorithm with interface prediction and correction for spherical geometric transport equation

When solving transport equation by the discrete ordinates method, the solution procedure must accord with the moving direction of particle due to the stability restriction. Thus it results in a strong correlation among these unknown variables, and the intrinsic serial nature of the corresponding algorithmic procedure becomes the bottleneck for transport equation calculations on large-scale parallel computers. The conventional parallel sweep method has restrictive but in no means high degree of parallelism for two and three spatial dimensional problems, and it has no spatial parallel degree for one-dimensional problems. In this paper, a spatial domain decomposition method is adopted in the computational domain, and different interface prediction and correction methods are introduced to solve the 1-D spherical geometric transport equation. It is natural to generalize to multidimension problems. In order to avoid producing negative flux, we employ the exponential method for variable discretization. The numerical experiments by using MPI show that our parallel method with explicit prediction and implicit correction has good precision, parallelism and simplicity.