Unstructured Discrete Ordinates Method Based on Radial Basis Function Approximation

Abstract

Numerical treatment of the boundary value problem with meshfree methods has been a popular research area in recent years. In the nuclear transport field, several applications of meshfree methods are employed to develop a solution for the neutron diffusion and transport equations. Among the meshfree methods, which based on radial basis function (RBF) approximation exhibits more advantages than others. By applying the RBF approximation, a flexible technique for discretizing the spatial variable of the neutron transport equation is provided without any requirements related to the shape of the unstructured mesh or the number of spatial dimensions. However, use of the RBF approximation without specified constraints on the number of data points used for constructing the approximation function may cause instability in the discrete equation system. In addition, it decreases the accuracy of the numerical solution near the geometric boundary. In this study, a numerical method is developed to solve the discrete ordinates equation (S_N) on unstructured mesh for neutron transport. Several benchmarks are implemented to evaluate the efficiency of the proposed method. Results are compared with analytical and reference results from the standard S_N method. The proposed method provides a stable and accurate solution for the transport problem with curved boundaries.