Abstract
In this paper, we introduce a regularization of the Pn equations for one-dimensional, slab geometries. These equations are used to describe particle transport through a material medium.Our regularization is based on a temporal splitting of fast and slow dynamics in the Pn system. It uses ideas first introduced in [S. Jin, SIAM J. Sci. Comput., 21 (1999), pp. 441-454] for 2 X 2 systems to address systems of arbitrary size and with spatially varying media. The regularization captures the proper diffusion limit in diffusive regimes but behaves like the original Pn system in streaming regimes. It also allows for larger times steps in diffusive regimes, when the original Pn system is stiff. In particular, for simulations in which the computational mesh does not resolve the particle mean free path, the regularization admits a simple scheme with no stability restrictions on the time step.
Original language | English |
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Pages (from-to) | 1497-1524 |
Number of pages | 28 |
Journal | Multiscale Modeling and Simulation |
Volume | 7 |
Issue number | 4 |
DOIs | |
State | Published - 2009 |
Externally published | Yes |
Keywords
- Diffusive relaxation
- Operator splitting
- Pn equations
- Stiff relaxation
- Temporal regularization
- Transport theory