Abstract
In this work, we prove rigorous error estimates for a hybrid method introduced in [Hauck, Cory D, and Ryan G McClarren. 2013. Multiscale Modeling & Simulation 11 (4):1197–1227] for solving the time-dependent radiation transport equation (RTE). The method relies on a splitting of the kinetic distribution function for the radiation into uncollided and collided components. A high-resolution method (in angle) is used to approximate the uncollided components and a low-resolution method is used to approximate the collided component. After each time step, the kinetic distribution is reinitialized to be entirely uncollided. For this analysis, we consider a mono-energetic problem on a periodic domain, with constant material cross-sections of arbitrary size. To focus the analysis, we assume the high-resolution method for the uncollided equation is, in fact, an exact solution and the collided part is approximated in angle via a spherical harmonic expansion ((Formula presented.) method). Using a nonstandard set of semi-norms, we obtain estimates of the form (Formula presented.) where (Formula presented.) denotes the regularity of the solution in angle, (Formula presented.) and (Formula presented.) are scattering parameters, (Formula presented.) is the time-step before reinitialization, and C is a complicated function of (Formula presented.) (Formula presented.) and (Formula presented.) These estimates involve analysis of the multiscale RTE that includes, but necessarily goes beyond, usual spectral analysis. We also compute error estimates for the monolithic (Formula presented.) method with the same resolution as the collided part in the hybrid. Our results highlight the benefits of the hybrid approach over the monolithic discretization in both highly scattering and streaming regimes.
| Original language | English |
|---|---|
| Pages (from-to) | 316-349 |
| Number of pages | 34 |
| Journal | Journal of Computational and Theoretical Transport |
| Volume | 54 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2025 |
Funding
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, as part of their Applied Mathematics Research Program. The work was performed at the Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC under Contract No. De-AC05-00OR22725. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
Keywords
- Radiation transport
- hybrid method
- multiscale