Abstract
The numerical modeling of radiative transfer by the diffusion approximation can produce artificially damped radiation propagation if spatial cells are too optically thick. In this paper, we investigate this nonphysical behavior at external problem boundaries by examining the emissivity of the discretized diffusion approximation. We demonstrate that the standard cell-centered discretization produces an emissivity that is too low for optically thick cells, a situation that leads to the lack of radiation propagation. We then present a modified boundary condition that yields an accurate emissivity regardless of cell size. This modified boundary condition can be used with a deterministic calculation or as part of a hybrid transport-diffusion method for increasing the efficiency of Monte Carlo simulations. We also discuss the range of applicability, as a function of cell size and material properties, when this modified boundary condition is employed in a hybrid technique. With a set of numerical calculations, we demonstrate the accuracy and usefulness of this modified boundary condition.
| Original language | English |
|---|---|
| Pages (from-to) | 583-593 |
| Number of pages | 11 |
| Journal | Annals of Nuclear Energy |
| Volume | 33 |
| Issue number | 7 |
| DOIs | |
| State | Published - May 2006 |
| Externally published | Yes |
Funding
The work of the first and third authors (J.D.D. and D.B.C.) was performed under US Government contract W-7405-ENG-36 for Los Alamos National Laboratory, which is operated by the University of California for the US Department of Energy. The work of the second author (G.D.) was supported by the US Department of Energy Computational Science Graduate Fellowship Program as part of a practicum at Los Alamos National Laboratory.
| Funders | Funder number |
|---|---|
| US Department of Energy Computational Science | |
| U.S. Department of Energy | |
| University of California | |
| Los Alamos National Laboratory | |
| Government of South Australia | W-7405-ENG-36 |