Mesh-free method for numerical solution of the multi-group discrete ordinate neutron transport equation

Abstract

The finite element method (FEM) is a widely-used method to solve neutron transport equation in an arbitrary domain, but in order to ensure the accuracy of solution a re-meshing process is often required and some regions of the domain need to be meshed with finer meshes and consequently the whole domain should be re-meshed again. To overcome this problem of the FEM we have applied Mesh Free (MFree) method for the solution of the neutron transport equation. In mesh free technique, there is no need to regenerate finer meshes to ensure the accuracy of the solution and only the number of nodes in local domains is increased. MFree method is flexible for distributing arbitrary and irregular nodes, therefore this method can be easily applied for high absorbent regions in the nuclear reactor problems. We have developed a program, named SNMF, which solves discrete ordinate neutron transport equation, using mesh free techniques based on Radial Point Interpolation Method (RPIM). To validate SNMF program some test problems have been modeled. For the first time, the application of MFree method is examined to solve neutron transport equation. Our results show that mesh free discrete ordinate method can be used as an efficient and accurate method to solve neutron transport equation without hardness and limitations of finite element methods.