One-Dimensional Models for Time-Dependent Transport in Solid Cylinders

Journal Article · Tue Dec 18 00:00:00 EST 2018 · Journal of Computational and Theoretical Transport

DOI:https://doi.org/10.1080/23324309.2018.1481434· OSTI ID:1492609

McClarren, Ryan Gerard ^[1]; Long, Alex Roberts ^[2]

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1. Univ. of Notre Dame, IN (United States). Dept. of Aerospace and Mechanical Engineering
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computational Physics and Methods Group (CCS-2)

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. Here, 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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1492609
• Report Number(s): LA-UR--18-22559
• Journal Information: Journal of Computational and Theoretical Transport, Journal Name: Journal of Computational and Theoretical Transport Journal Issue: 4-6 Vol. 47; ISSN 2332-4309
• Publisher: Taylor and Francis
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Marshak waves
Particle transport
mathematical modeling