A discontinuous finite element method based on B-spline wavelet on the interval for solving first-order neutron transport equation with discrete ordinate (SN) angular discretisation

•A new discontinuous Galerkin finite element method (DGFEM) based on B-spline wavelet on the interval has been developed to solve the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretization for the first time.•Under the same cells, the accuracy of the new method is as good as that of second order T-DGFEM for eigenvalue problem and up to that of third order T-DGFEM for fixed source problem. In this paper, a discontinuous Galerkin finite element method (DGFEM) based on B-spline wavelet on the interval (BSWI) is developed and applied to solve the first-order neutron transport equation with discrete ordinate (SN) angular discretization. Then, using the scaling function of BSWI function as the basis function instead of the usual Lagrange basis function, the neutron transport equation based on BSWI discontinuous finite element is derived. Owing to the high precision characteristic of BSWI function, the method proposed in this paper can obtain fast convergence and statistical numerical accuracy under the condition that few spatial elements are used, and comparing with the results of the traditional discontinuous finite element method. Finally, some numerical examples are utilized to verify the accuracy and efficiency of the proposed method, and the results show that the method has high efficiency, reliable and stability, and the calculation accuracy is higher than that of the conventional discontinuous finite element method.