(A) study on CMFD acceleration of FEM scheme for multi-group neutron diffusion equations

Abstract

A study on Coarse Mesh Finite Difference (CMFD) and p-CMFD accelerations based on the Finite Element Method (FEM) has been conducted for multi-group neutron diffusion equations. The direct application of two-node CMFD acceleration into FEM based neutron diffusion equation gives an inconsistent result due to the non-conservative discretization property of FEM. The Pseudo Absorption Cross Section (PAXS) scheme is introduced into the two-node CMFD main equation to enforce the neutron local balance of the FEM-based CMFD equations. It was observed that the implementation of PAXS into two-node CMFD and p-CMFD results in the consistent solution and improvement of computing performance. Another way to improve the computing performance is by utilizing the parallel calculation. As one-node CMFD preserved the surface current and flux in the interface, it is highly suitable for parallel computing. The direct application of one-node CMFD to the parallel FEM based neutron diffusion equation gives an inconsistent result. Furthermore, the one-node CMFD net current calculated from the outgoing partial current of adjacent local fine mesh, which is will be used to be the local parallel FEM boundary condition, could not give the converged solution. The implementation of PAXS into one- node CMFD helps the one-node CMFD converged although the solution is still inconsistent. An alternating one-node CMFD for parallel calculation was proposed to solve the problem in this work. The alternating one-node CMFD consists of two CMFD levels that do not have the same interface position and the global iteration is done alternatingly by the two CMFD levels. The alternating one-node CMFD net current is calculated inherently from the local fine mesh using the FEM approach.