An Accurate Globally Conservative Subdomain Discontinuous Least-squares Scheme for Solving Neutron Transport Problems

TL;DR

This paper introduces a subdomain discontinuous least-squares scheme for neutron transport that maintains global conservation and improves accuracy across material interfaces, especially in heterogeneous problems.

Contribution

The paper proposes a novel SDLS method that ensures global conservation and handles sharp interfaces more accurately than traditional LS schemes.

Findings

High accuracy in scalar flux for fixed-source problems

Effective in k-eigenvalue problems with heterogeneous materials

Compared favorably with other numerical methods

Abstract

In this work, we present a subdomain discontinuous least-squares (SDLS) scheme for neutronics problems. Least-squares (LS) methods are known to be inaccurate for problems with sharp total-cross section interfaces. In addition, the least-squares scheme is known not to be globally conservative in heterogeneous problems. In problems where global conservation is important, e.g. k-eigenvalue problems, conservative treatment must be applied. We, in this study, proposed a SDLS method that retains global conservation. Such a method resembles the LS formulation in each subdomain without material interface and differs from LS in that an additional least-squares interface term appears for each interface. Scalar flux is continuous in each subdomain with continuous finite element method (CFEM) while discontinuous on interfaces for every pair of contiguous subdomains. SDLS numerical results are compared with those obtained from other numerical methods with test problems having material interfaces. High accuracy of scalar flux in fixed-source problems and $k_\mathrm{eff}$ in eigenvalue problems are demonstrated.