Abstract
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.
| Original language | English |
|---|---|
| Pages (from-to) | 17-37 |
| Number of pages | 21 |
| Journal | Journal of Computational Physics |
| Volume | 262 |
| DOIs | |
| State | Published - Apr 1 2014 |
Funding
The authors would like to thank the anonymous referees who provided important feedback to improve the manuscript. We are grateful to the National Center for Computational Science at ORNL for access to their internal high performance computing resources and to James Schwarzmeier from CRAY Inc. for providing access to a CRAY XE6 system for extensive testing of the non-equilibrium radiation diffusion application presented in this paper. Zhen Wang would like to acknowledge support from the Mathematical, Information, and Computational Sciences Division, Office of Advanced Scientific Computing Research, U.S. Department of Energy, Mark Berrill would like to acknowledge support from the Eugene P. Wigner Fellowship, and Bobby Philip would like to acknowledge funding support from the Oak Ridge Leadership Computing facility all at Oak Ridge National Laboratory, managed by UT-Battelle , LLC , for the U.S. Department of Energy under Contract DE-AC05-00OR22725 .
Keywords
- Adaptive mesh refinement
- Implicit methods
- Jacobian Free Newton-Krylov
- Multilevel solvers
- Non-equilibrium radiation diffusion
- Timestep control
