The evaluation of different trial shape functions applied in Spectral Element Method in analysis of multi-group Pn transport equation

The SEM approach is an advanced numerical technique based on combination of high-order Finite Element Method (FEM) and spectral methods, which benefits both from geometric flexibility of Finite Element Method and high accuracy of spectral methods. In this study, the neutron transport equation has been converted into weak form obtained by Generalized Least Squares Method (GLSM) and implementation K+ variational principle. In order to analyze the spatial-wise and the angular-wise integrals of K+ variational method, the angular part of flux has been developed via spherical harmonics expansion while Spectral Element Method has been applied in spatial part of flux. Spectral nodal discretization and trial function expansion has been implemented via different orthogonal polynomials. In present work, a comparison among different basis shape functions (trial functions) applied in SEM approach has been illustrated. Therefore, a general comparison between the capability of nodal discretization and solution accuracy of different polynomials can be represented. The incorporation of SEM with variety of nodal discretization of polynomials would give an opportunity to study the behavior of each of polynomials in numerical calculations.