A new continuous finite element SN method for solving first-order neutron transport equation

Abstract

A continuous finite element method (FEM) based on B-spline wavelet on the interval (BSWI) is proposed to solve the first-order neutron transport equation with discrete ordinate (SN) angular discretization. Two technologies are applied in this method, one of technologies is that the streamline upwind Petrov-Galerkin (SUPG) method is utilized to stabilize the first-order neutron transport equation when the FEM is used. Another is that the scaling functions of BSWI are applied to replace the usual Lagrange basis function. Based on the above two technologies, the stabilized weak form of neutron transport equation applying the SUPG technology based on BSWI is derived. Finally, some numerical examples are utilized to verify the proposed method. The results demonstrate that the method can treat the void region problem, and compared the FEM with SUPG technology, it can obtain fast convergence and numerical precision under the condition of much less grid. Overall, this method has good accuracy, high computational efficiency and wide application.