Computational techniques for fluid dynamics
Computational techniques for fluid dynamics
CVODE, a stiff/nonstiff ODE solver in C
Computers in Physics
SIAM Journal on Scientific Computing
Blowup in diffusion equations: a survey
Journal of Computational and Applied Mathematics - Special issue: nonlinear problems with blow-up solutions: applications and numerical analysis
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
Studies on the accuracy of time-integration methods for the radiation-diffusion equations
Journal of Computational Physics
A comparison of implicit time integration methods for nonlinear relaxation and diffusion
Journal of Computational Physics
Second-order splitting schemes for a class of reactive systems
Journal of Computational Physics
On the accuracy of operator splitting for the monodomain model of electrophysiology
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Journal of Computational Physics
Journal of Scientific Computing
An exponential integrator for advection-dominated reactive transport in heterogeneous porous media
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations
Journal of Computational Physics
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In this study we present numerical experiments of time integration methods applied to systems of reaction-diffusion equations. Our main interest is in evaluating the relative accuracy and asymptotic order of accuracy of the methods on problems which exhibit an approximate balance between the competing component time scales. Nearly balanced systems can produce a significant coupling of the physical mechanisms and introduce a slow dynamical time scale of interest. These problems provide a challenging test for this evaluation and tend to reveal subtle differences between the various methods. The methods we consider include first- and second-order semi-implicit, fully implicit, and operatorsplitting techniques. The test problems include a prototype propagating nonlinear reaction--diffusion wave, a non-equilibrium radiation--diffusion system, a Brusselator chemical dynamics system and a blow-up example. In this evaluation we demonstrate a "split personality" for the operator-splitting methods that we consider. While operatorsplitting methods often obtain very good accuracy, they can also manifest a serious degradation in accuracy due to stability problems.