Analysis of a Monte Carlo method for nonlinear radiative transfer
Journal of Computational Physics
SIAM Journal on Scientific Computing
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Numerical analysis of time integration errors for nonequilibrium radiation diffusion
Journal of Computational Physics
Transient Simulation of Silicon Devices and Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Hi-index | 31.45 |
We apply the Trapezoidal/BDF2 (TR/BDF2) temporal discretization scheme to nonlinear grey radiative diffusion. This is a scheme that is not well-known within the radiation transport community, but we show that it offers many desirable characteristics relative to other second-order schemes. Several nonlinear variants of the TR/BDF2 scheme are defined and computationally compared with the Crank-Nicholson scheme. It is found for our test problems that the most accurate TR/BDF2 schemes are those that are fully iterated to nonlinear convergence, but the most efficient TR/BDF2 scheme is one based upon a single Newton iteration. It is also shown that neglecting the contributions to the Jacobian matrix from the cross-sections, which is often done due to a lack of smooth interpolations for tabular cross-section data, has a significant impact upon efficiency.