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

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 LS scheme is known not to be globally conservative in heterogeneous problems. In problems where global conservation is important, e.g., k-eigenvalue problems, a conservative treatment must be applied. In this study, we propose an SDLS method that retains global conservation and, as a result, gives high accuracy on eigenvalue problems. Such a method resembles the LS formulation in each subdomain without a material interface and differs from LS in that an additional LS interface term appears for each interface. The scalar flux is continuous in each subdomain with the continuous finite element method while discontinuous on interfaces for every pair of contiguous subdomains. The 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 in eigenvalue problems is demonstrated.