A First collision source method using spherical harmonics method for arbitrary shape and order finite element mesh

Abstract

The discrete ordinates (SN) method is a highly effective and accurate angular discretization method for the neutron transport equation, but suffers from the inherent ray effect in low-scattering regions. The first collision source (FCS) method employing the methods without ray effect to obtain the uncollided flux is a common ray effect mitigation technique. In this paper, a novel FCS method using the spherical harmonics (PN) method to calculate the uncollided flux is proposed. The PN for the first collision source (PN-FCS) method possesses distinctive advantages in several aspects: (1) it can be applied in the problem containing reflective boundary conditions that are difficult to handle with traditional FCS method, (2) it uses the discontinuous Galerkin method to perform spatial discretization, and thus can be easily applied in arbitrary shape and order finite element meshes, (3) it can be effectively calculated in parallel on distributed meshes, (4) the accuracy and computational cost can be flexibly adjusted. Besides, the filter technique is adopted to improve the performance of the PN method in stream-dominated regions. The PN-FCS method has been implemented in two- and three-dimensional neutron transport code and tested by various testing problems. Numerical results show that the PN-FCS method can effectively mitigate the ray effect.