  Second Moment Methods (SMMs) are developed that are consistent with the
Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates
(or \Sn) transport equations. The low-order (LO) diffusion system of equations
is discretized with fully consistent \Pone, Local Discontinuous Galerkin (LDG),
and Interior Penalty (IP) methods. A discrete residual approach is used to
derive SMM correction terms that make each of the LO systems consistent with
the high-order (HO) discretization. We show that the consistent methods are
more accurate and have better solution quality than independently discretized
LO systems, that they preserve the diffusion limit, and that the LDG and IP
consistent SMMs can be scalably solved in parallel on a challenging,
multi-material benchmark problem.
