Hybrid P_N-S_N 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 P_N-S_N 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 S_N Lagrange interpolation method on the unit sphere is proposed. The discrete P_N interface condition with upwinding method for coupling the S_N solution is desired. Numerical results indicate that the interface conditions give the expected convergence.