CVODE, a stiff/nonstiff ODE solver in C
Computers in Physics
Journal of Computational Physics
A semi-implicit numerical scheme for reacting flow: II. stiff, operator-split formulation
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Numerical Modeling in Applied Physics and Astrophysics
Numerical Modeling in Applied Physics and Astrophysics
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Studies of the accuracy of time integration methods for reaction-diffusion equations
Journal of Computational Physics
Self-adaptive time integration of flux-conservative equations with sources
Journal of Computational Physics
Stability of semidiscrete formulations for elastodynamics at small time steps
Finite Elements in Analysis and Design
Numerical analysis of time integration errors for nonequilibrium radiation diffusion
Journal of Computational Physics
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Journal of Computational Physics
Fully implicit 1D radiation hydrodynamics: Validation and verification
Journal of Computational Physics
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
Journal of Computational Physics
Hi-index | 31.49 |
The governing equations for the radiation-diffusion approximation to radiative transport are a system of highly nonlinear, multiple time-scale, partial-differential equations. The numerical solution of these equations for very large-scale simulations is most often carried out using semi-implicit linearization or operator-splitting techniques. These techniques do not fully converge the nonlinearities of the system so as to reduce the cost and complexity of the transient solution at each time step. For a given time-step size, this process exchanges temporal accuracy for computational efficiency. This study considers the temporal-accuracy issue by presenting detailed numerical-convergence studies for problems related to radiation-diffusion simulations. In this context a particular spatial discretization based on a Galerkin finite-element technique is used. The time-integration methods that we consider include: fully implicit, semi-implicit, and operator-splitting techniques. Results are presented for the relative accuracy and the asymptotic order of accuracy of the various methods. The results demonstrate both first-order and second-order asymptotic order of accuracy for the fully implicit, semi-implicit, and the operator-splitting schemes. Additionally a second-order operatorsplitting linearized-diffusion method is also presented.