Algebraic Stabilization of Explicit Numerical Integration for Extremely Stiff Reaction Networks
- ORNL
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.
- Research Organization:
- Oak Ridge National Laboratory (ORNL)
- Sponsoring Organization:
- SC USDOE - Office of Science (SC)
- DOE Contract Number:
- AC05-00OR22725
- OSTI ID:
- 1051431
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 16 Vol. 232; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Explicit Integration of Extremely Stiff Reaction Networks: Partial Equilibrium Methods
Explicit Integration of Extremely Stiff Reaction Networks: Quasi-Steady-State Methods