Semi-implicit time integration for P{sub N} thermal radiative transfer
- Reactor Analysis Group, Oak Ridge National Laboratory, P.O. Box 2008, MS 6172, Oak Ridge, TN 37831 (United States)
- Computational Physics Group (CCS-2), Los Alamos National Laboratory, P.O. Box 1663, MS D413, Los Alamos, NM 87545 (United States)
Implicit time integration involving the solution of large systems of equations is the current paradigm for time-dependent radiative transfer. In this paper we present a semi-implicit, linear discontinuous Galerkin method for the spherical harmonics (P{sub N}) equations for thermal radiative transfer in planar geometry. Our method is novel in that the material coupling terms are treated implicitly (via linearizing the emission source) and the streaming operator is treated explicitly using a second-order accurate Runge-Kutta method. The benefit of this approach is that each time step only involves the solution of equations that are local to each cell. This benefit comes at the cost of having the time step limited by a CFL condition based on the speed of light. To guarantee positivity and avoid artificial oscillations, we use a slope-limiting technique. We present analysis and numerical results that show the method is robust in the diffusion limit when the photon mean-free path is not resolved by the spatial mesh. Also, in the diffusion limit the time step restriction relaxes to a less restrictive explicit diffusion CFL condition. We demonstrate with numerical results that away from the diffusion limit our method demonstrates second-order error convergence as the spatial mesh is refined with a fixed CFL number.
- OSTI ID:
- 21159408
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 16 Vol. 227; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order
On an implicit ENO scheme