Assessment of the Lagrange Discrete Ordinates Equations for Three-dimensional Neutral Particle Transport

The Lagrange Discrete Ordinates (LDO) equations, developed by Ahrens as an alternative to the traditional discrete ordinates formulation, have been implemented in Denovo, a three-dimensional radiation transport code developed by Oak Ridge National Laboratory. The LDO equations retain the formal structure of the classical discrete ordinates equations typically used in radiation transport calculations but treat particle scattering in a different way. Solutions of the LDO equations have an interpolatory structure such that the angular flux can be naturally evaluated at directions other than the discrete ordinates used in arriving at the solutions, and the ordinates themselves may be chosen in a strategic way for the problem under consideration. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. We present scalar flux solutions of the LDO equations for a small number of test cases of interest and compare the results against flux solutions generated using standard quadrature types as well as against experimental flux measurements from a benchmark test case.