Abstract
We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite-volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.
| Original language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Multiscale Modeling and Simulation |
| Volume | 19 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2021 |
Funding
\ast Received by the editors December 10, 2019; accepted for publication (in revised form) August 27, 2020; published electronically January 7, 2021. https://doi.org/10.1137/19M1304520 Funding: This manuscript has been supported in part by UT-Battelle, LLC, under contract DE-AC0500OR22725 with the U.S. Department of Energy and by Los Alamos National Laboratory operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy under contract DEAC52-06NA25396. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, 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). This manuscript has been supported in part by UT-Battelle, LLC, under contract DE-AC0500OR22725 with the U.S. Department of Energy and by Los Alamos National Laboratory operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy under contract DEAC52-06NA25396. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, 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
- Diffusion limit
- Hybrid methods
- Radiation transport