  We present high-order, finite element-based Second Moment Methods (SMMs) for
solving radiation transport problems in two spatial dimensions. We leverage the
close connection between the Variable Eddington Factor (VEF) method and SMM to
convert existing discretizations of the VEF moment system to discretizations of
the SMM moment system. The moment discretizations are coupled to a high-order
Discontinuous Galerkin discretization of the Discrete Ordinates transport
equations. We show that the resulting methods achieve high-order accuracy on
high-order (curved) meshes, preserve the thick diffusion limit, and are
effective on a challenging multi-material problem both in outer fixed-point
iterations and in inner preconditioned iterative solver iterations for the
discrete moment systems. We also present parallel scaling results and provide
direct comparisons to the VEF algorithms the SMM algorithms were derived from.
