Algebraic stabilization of explicit numerical integration for extremely stiff reaction networks

Authors:
Mike Guidry
Affiliations:
Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996-1200, USA and Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA and Computer Science and M ...
Venue:
Journal of Computational Physics
Year:
2012

Citing 8
Cited 0

Direct methods for sparse matrices

Direct methods for sparse matrices
Numerical methods for ordinary differential systems: the initial value problem

Numerical methods for ordinary differential systems: the initial value problem
An evaluation of explicit pseudo-steady-state approximation schemes for stiff ODE systems from chemical kinetics

Journal of Computational Physics
Explicit methods for stiff ODEs from atmospheric chemistry

NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
Improved Quasi-Steady-State-Approximation Methods for Atmospheric Chemistry Integration

SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)

LAPACK Users' guide (third ed.)
A quasi-steady state solver for the stiff ordinary differential equations of reaction kinetics

Journal of Computational Physics
Numerical Initial Value Problems in Ordinary Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

Quantified Score

Hi-index	31.45

Visualization

Abstract

In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the numerical integration. The stabilizing algebra differs essentially for systems well-removed from equilibrium and those near equilibrium. Explicit asymptotic and quasi-steady-state methods that are appropriate when the system is only weakly equilibrated are examined first. These methods are then extended to the case of close approach to equilibrium through a new implementation of partial equilibrium approximations. Using stringent tests with astrophysical thermonuclear networks, evidence is provided that these methods can deal with the stiffest networks, even in the approach to equilibrium, with accuracy and integration timestepping comparable to that of implicit methods. Because explicit methods can execute a timestep faster and scale more favorably with network size than implicit algorithms, our results suggest that algebraically-stabilized explicit methods might enable integration of larger reaction networks coupled to fluid dynamics than has been feasible previously for a variety of disciplines.