A mesh-free treatment for even parity neutron transport equation

Abstract

Common family of numerical methods such as finite element and finite difference involve the discretization of domain into regular grids or meshes. Mesh generation and re-meshing process, however, for obtaining required accuracy are complicated and time-consuming. Recently, Mesh Free (MFree) methods have been developed to overcome the drawbacks of such conventional numerical methods. In the present work, a novel approach is developed for solving multi-group neutron transport equation in two-dimensional X-Y geometry based on a mesh free scheme using the Radial Point Interpolation Method (RPIM). The K+ principle which is an extremum variational principle for solving even parity neutron transport equation is our choice to implement RPIM. The directional dependence of even-parity angular flux is expanded by the spherical harmonic polynomials which leads to PN method. The multi-quadrics radial basis function is used to construct the RPIM shape functions for spatial approximation of angular flux to obtain the discretized MFree weak-form of neutron transport equation. As the RPIM shape functions possess the Kronecker delta function property, essential boundary conditions is enforced as efficiently as in the finite element method (FEM). The obtained results are compared with some mesh-based methods such as conventional finite element method to evaluate the performance of the presented approach. It is demonstrated that the proposed method is robust, stable, reliable and efficient for treatment of neutron transport.