Graduate Thesis Or Dissertation
 

Flux-limited diffusion theory for spatially discretized equations : a discretized derivation of Levermore-Pomraning FLDT

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  • Spatially discretized diffusion approximation equations are derived directly from spatially discretized radiation transport equations in 1-D slab geometry. Derivations for isotropic diffusion theory (IDT) and Levermore-Pomraning's flux-limited diffusion theory (FLDT) are applied to lumped linear discontinuous (LLD) transport equations. We find that the (energy density) solution is continuous across the edge for EDT. For FLDT, we find that the intensity may he discontinuous across a cell edge; this doubles the number of points that traditionally need to be solved for in a diffusion approximation. The FLDT derivation produces unique discretized flux-limited diffusion equations. We produced a numerical scheme for these FLDT equations that includes a new iteration on the flux-limiting parameter and a local iteration on the edge discontinuities. Numerical results indicate that this approach is an improvement over standard numerical FLDT discretization schemes.
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