Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems

Authors:
David L. Ropp;John N. Shadid
Affiliations:
Northrop Grumman Corporation, Electronic Systems, 7323 Aviation Blvd., Linthicum, MD 21240-2001, United States;Computational Sciences R&D Group, MS 0316, P.O. Box 5800, Sandia National Laboratories, Albuquerque, NM 87185-0316, United States
Venue:
Journal of Computational Physics
Year:
2009

Citing 10
Cited 4

Numerical methods for ordinary differential systems: the initial value problem

Numerical methods for ordinary differential systems: the initial value problem
CVODE, a stiff/nonstiff ODE solver in C

Computers in Physics
Linearly implicit splitting methods for higher space-dimensional parabolic differential equations

Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
A semi-implicit numerical scheme for reacting flow: II. stiff, operator-split formulation

Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case

Journal of Computational Physics
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations

Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
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
Studies of the accuracy of time integration methods for reaction-diffusion equations

Journal of Computational Physics
Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems

Journal of Computational Physics

A second order self-consistent IMEX method for radiation hydrodynamics

Journal of Computational Physics
Operator splitting implicit integration factor methods for stiff reaction-diffusion-advection systems

Journal of Computational Physics
A positivity-preserving finite element method for chemotaxis problems in 3D

Journal of Computational and Applied Mathematics
Multiphysics simulations: Challenges and opportunities

International Journal of High Performance Computing Applications

Quantified Score

Hi-index	31.46

Visualization

Abstract

This brief paper presents an A-stability result for operator splitting type time integration methods applied to advection-diffusion-reaction equations with possibly indefinite source terms. These results extend our earlier work on diffusion-reaction systems [D.L. Ropp, J.N. Shadid, Stability of operator splitting methods for systems with indefinite operators: reaction-diffusion systems, J. Comput. Phys. 203 (2) (2005) 449-466]. The A-stability result presents sufficient conditions that control both low and high wave number instabilities. A corollary shows that if L-stable methods are used for the diffusion term the high wave number instability will be controlled more easily. Numerical results are presented that verify second-order convergence for the operator splitting methods and demonstrate control of instabilities on a chemotaxis problem by use of an L-stable diffusion integrator.