Hybrid PN-SN with Lagrange multiplier and upwinding for the multiscale transport capability in Rattlesnake

Two interface conditions, the Lagrange multiplier method and the upwinding method, for hybrid PN-SN calculations are proposed for the self-adjoint angular flux (SAAF) formulation of the transport equation using the continuous finite element method (FEM) for spatial discretization. These interface conditions are implemented in Rattlesnake, the radiation transport application built on MOOSE, for the on-going multiscale transport simulation effort at INL. For smoothing the solution at the interface for the Lagrange multiplier method, a SN Lagrange interpolation method on the unit sphere is proposed. The discrete PN interface condition with upwinding method for coupling the SN solution is desired. Numerical results indicate that the interface conditions give the expected convergence.