One-Dimensional Models for Time-Dependent Transport in Solid Cylinders. Issue 4 (19th September 2018)

• Record Type: Journal Article
• Authors: McClarren, Ryan G.; Long, Alex R.
• Is Part Of: Journal of computational and theoretical transport. Volume 47:Issue 4/6(2018)
• Page Start: 364
• Page End: 377
• Publication Date: 2018-09-19
• Subjects: Particle transport -- mathematical modeling; Transport theory -- Periodicals; Statistical physics -- Periodicals; Statistical physics; Transport theory; Periodicals; 530.138
• DOI: 10.1080/23324309.2018.1481434
• Languages: English
• ISSNs: 2332-4309

Abstract

Abstract: We present a set of 1-D transport models for solid cylinders of material irradiated with particles on the axial ends. The models are based on 1-D models originally developed for evacuated ducts with reflecting walls. The goal of this work is to show that 1-D models can be used for time-dependent transport in solid cylinders. A future use of this approach will apply these models to the high-energy density physics problem of a Marshak wave propagating down a cylindrical foam or other experiments. The models we present use a Galerkin procedure to project the radial dependence of the 3-D transport equation onto an expansion in terms of polynomials. Results demonstrate that for steady state problems with low scattering ratios, a three-basis function expansion can adequately capture the 3-D solution as computed via Monte Carlo. Smaller number of basis functions did not result in adequate solutions. As the radius of the cylinder increases, the 1-D model is more effective. Results from time dependent problems indicate that the 1-D models move particles too fast down the cylinder at early times, but are accurate on the order of 10 or more mean-free times. Our results indicate that 1-D models may be effective in modeling 2-D Marshak waves, but further work is necessary to answer this question.