ENTRANS: A platform for finite elements modeling of 3D neutron transport equation, Part II. Multidimensional implementation

Abstract

Practical challenges concerning the solution of multi-dimensional even parity Neutron Transport Equation (NTE) is investigated in depth. Semi-analytic approach is provided by analytic integration of angular matrices appeared through expansion of even parity angular flux density, ψ+(r,Ω), via Spherical Harmonics Polynomials (SHPs). Spatial variable treatment is carried out by using Finite Element Method, FEM, for arbitrary geometries (slab, spherical and cylindrical), 2D (XY) and 3D (XYZ) spaces along implementing high order elements. Furthermore, an analytic expression for a bare boundary oriented in any direction in 2D geometry is derived. Implementation of exact reflective boundary condition in 2D and 3D geometries is described, too.As a critical step, to provide a high quality mesh for each simulation in the most automated way Gambit pre-processor is invoked as the auxiliary geometry sketcher-smasher tool for our developed Even parity Neutron TRANSport code, ENTRANS.The aim of this paper is to demonstrate the capability of ENTRANS code for criticality, fixed source and shielding calculations along using Gambit mesh generator to relax representation of complicated geometries. To validate the ENTRANS, various challenging simulations in 1, 2, and 3D geometries are assessed against related representative benchmarks. The results confirm good agreement between ENTRANS and reported data.