SNA-MC-abstract.txt

Radiation shielding is an important and interesting problem. Hybrid radiation transport methods that use deterministic solutions to speed up stochastic calculations often take long times to converge for shielding problems with highly anisotropic radiation streaming pathways. In this work, we investigate using a unique deterministic formulation, the Lagrange Discrete Ordinates (LDO) equations, for Monte Carlo variance reduction (VR) parameter generation in hybrid methods. The LDO equations retain the formal structure of the traditional discrete ordinates approximation of the Boltzmann transport equation while handling the angular variable and particle scattering in a unique fashion. The LDO equations' solutions 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 those discrete ordinates at which the problem is solved may be chosen in a strategic way. Of particular interest is that the LDO equations have been shown to mitigate ray effects at increased angular resolutions. These properties suggest that using the LDO formulation in hybrid methods may improve their performance in shielding problems where anisotropic behavior is important.

Here, we investigate using the LDO equations' scalar flux solutions in the Consistent Adjoint Driven Importance Sampling (CADIS) and Forward Weighted (FW)-CADIS methods for Monte Carlo variance reduction parameter generation. Monte Carlo calculations and Figures of Merit using VR parameters from the LDO equations are compared against those using VR parameters from standard quadrature set types for a collection of engineering-scale test problems. The problems chosen, two neutron transport and one photon transport, have angular streaming features that challenge the CADIS and FW-CADIS methods. Using the LDO equations to create VR parameters with the FW-CADIS method gave better performance in many cases, especially for the photon test problem. When using an LDO formulation for Monte Carlo VR parameter generation, we suggest using a fairly coarse angular mesh of 36 to 81 discrete ordinates for neutron or photon transport problems in the FW-CADIS context, a coarse angular mesh of 16 to 81 discrete ordinates for neutron transport with the CADIS method, and the finest available angular mesh for photon transport in the CADIS context.