A Consistent CMFD Formulation for the Acceleration of Neutron Transport Calculations Based on the Finite Element Method

This paper presents the method and performance of a coarse-mesh finite difference (CMFD) scheme for accelerating neutron transport calculations based on the finite element method (FEM). The transport solution based on FEM does not satisfy the neutron balance exactly because FEM yields a nonconservative discretization. A modified CMFD formulation has been developed to correct the limitation of the conventional CMFD that is applicable only to neutronics solvers with a conservative discretization. A consistent CMFD problem for the transport solution based on FEM is constructed by enforcing the neutron balance in each coarse mesh by introducing a pseudo absorption cross section, and the well-established alternating solution process of CMFD and transport calculations is employed to accelerate source convergence. The applicability of the modified CMFD scheme to transport calculation based on FEM was first tested for a one-dimensional, discrete ordinates (S_N), discontinuous FEM. The performance of CMFD acceleration was then investigated with a two-dimensional/three-dimensional method of characteristic transport solver for thermal and fast reactor problems with various core sizes. It was observed that the consistent CMFD scheme could improve the computational efficiency of eigenvalue calculation significantly in the framework of a transport solver with fission source iteration.