Mesh-free RBF collocation method to solve the multi-group SN neutron transport equation in arbitrary domains

Abstract

Generally for numerical solution of the differential equations the mesh generation process is a major problem in classical mesh-based methods, especially in irregular domains. Contrary to the meshed based methods, Mesh Free (MFree) methods have been developed to avoid mesh generation. In the MFree methods a set of scattered nodes is used without requiring any mesh grid. So in this work the application of MFree collocation method is examined to solve SN neutron transport equation. The MFree collocation method uses the formulation of strong form which is truly mesh less method. Since MFree method is flexible for distributing arbitrary and irregular nodes, this method can be easily applied for high heterogeneous nuclear reactor problems with complicated geometry. To validate the proposed method some test problems including regular and irregular geometries have been modeled. Our results show that the mesh free collocation method can be used for discrete ordinate neutron transport equation as an efficient and accurate method without hardness and limitations of the mesh-based methods like finite element method.