Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes II
Journal of Computational Physics
A linear-discontinuous spatial differencing scheme for Sn radiative transfer calculations
Journal of Computational Physics
An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
SIAM Journal on Numerical Analysis
Asymptotic analysis of a computational method for time- and frequency- dependent radiative transfer
Journal of Computational Physics
Uniform Stability of a Finite Difference Scheme for Transport Equations in Diffusive Regimes
SIAM Journal on Numerical Analysis
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Journal of Computational Physics
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Two-dimensional time dependent Riemann solvers for neutron transport
Journal of Computational Physics
Spatial discretizations for self-adjoint forms of the radiative transfer equations
Journal of Computational Physics
On solutions to the Pn equations for thermal radiative transfer
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Second-order time evolution of PN equations for radiation transport
Journal of Computational Physics
Robust and accurate filtered spherical harmonics expansions for radiative transfer
Journal of Computational Physics
SIAM Journal on Scientific Computing
A realizability-preserving discontinuous Galerkin method for the M1 model of radiative transfer
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
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"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.