A spherical harmonics-Finite element discretization of the self-adjoint angular flux neutron transport equation

The spherical harmonics (P_N) method is widely used in solving the neutron transport equation, but it has some disadvantages. One of them comes from the complexity of the P_N equations. Another one comes from the difficulty of dealing with the vacuum boundary condition exactly. In this paper, the P_N method is applied to the self-adjoint angular flux (SAAF) neutron transport equation and a set of P_N moments equations coupled with each other are obtained. An iterative method is utilized to decouple them and solve them moment by moment. The corresponding vacuum boundary condition is derived based on the Marshak boundary condition. The spatial variables are discretized on unstructured-meshes by use of the finite element method (FEM). The numerical results of several problems demonstrate that this method can provide high precision results and avoid the ray effect, which appears in the discrete ordinate (S_N) method, with relatively high computational efficiency.