The finite element spherical-harmonics method is applied to the solution of the Kobayashi 3D benchmark problems. In particular, we evaluate the surface radiation exchange method based on raytracing which has been developed to circumvent the difficulty caused to the second-order, even-parity formulation by low-density regimes. This method brings several advantages which include obviating the need to explicitly solve the problem in voided regions and improving accuracy of the solution for a given order of angular approximation. Results produced by the computer code EVENT are presented for the six cases proposed. Comparisons with reference solutions show that the hybrid scheme can solve to reasonable accuracy most cases with relatively modest space-angle resolution. For the more difficult cases involving streaming in purely absorbing media, noticeable discrepancies were observed, but this indicated the need for a more judicious space-angle refinement (not attempted) rather than any deficiency of the hybrid scheme itself.
De Oliveira, C. R. E., Eaton, M. D., Umpleby, A. P., & Pain, C. C. (2001). Finite element-spherical harmonics solutions of the 3D Kobayashi benchmarks with ray-tracing void treatment. Progress in Nuclear Energy, 39(2), 243–261. https://doi.org/10.1016/S0149-1970(01)00015-4