Benchmark Solutions for Radiation Transport in Stochastic Media with Inhomogeneous Material Statistics
- Univ. of New Mexico, Albuquerque, NM (United States). Dept. of Nuclear Engineering
Accurately solving implicit Monte Carlo (IMC) thermal photon transport problems with mixed material cells is important in realistic applications. The production IMC package at LLNL treats mixed material cells arising from ALE remap and hydrodynamics using the same approximate model. The new Imp IMC thermal photon transport package currently under development has both a material interface reconstruction (MIR) algorithm and a Levermore-Pomraning (LP) stochastic medium algorithm for treating mixed material cells. Existing stochastic medium algorithms for treating mixed material cells in IMC lack a complete theoretical basis. The IMC LP algorithm implementation has been demonstrated to reproduce published deterministic LP solutions for the particular case of spatially homogeneous material statistics. Realistic simulations will include spatially inhomogeneous material statistics (material mean chord lengths). In a previous investigation, the LP-model for transport in binary stochastic media in rod geometry was generalized to accommodate spatially varying material chord lengths, i.e., the mixing statistics were allowed to be nonhomogeneous. Analytical solutions were obtained and used to produce a verifi cation suite for the Imp IMC Levermore-Pomraning implementation for different spatial variations of the chord lengths. However, the accuracy of the LP model when the mixing statistics are nonhomogeneous has not been assessed and leaves open the question of whether local accuracy is improved or further degraded when chord lengths are not uniform. This shortcoming is rectifi ed here by developing benchmark analytic solutions for transport in binary Markovian stochastic mixtures in rod geometry with nonhomogeneous mixing statistics, using spatially varying chord lengths considered in the previous investigation based on the LP model. Methods for sampling a nonhomogeneous Poisson process (NHPP) are first described and used to construct individual realizations of the binary mixtures in rod geometry. Analytic solutions are then obtained for the forward and backward directed fluxes on a given realization, now viewed as a deterministic medium with alternating layers of the two materials with known interface locations. Finally, material averaged scalar fluxes are obtained using these sampling schemes with spatially linear and quadratic chord lengths and used to assess the accuracy of the previously obtained LP-model results.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1634291
- Report Number(s):
- LLNL-SR-811823; 1018758; TRN: US2200888
- Country of Publication:
- United States
- Language:
- English
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