Explicit Integration of Extremely Stiff Reaction Networks: Partial Equilibrium Methods

Journal Article · Tue Jan 01 00:00:00 EST 2013 · Computational Science & Discovery

DOI:https://doi.org/10.1088/1749-4699/6/1/015003· OSTI ID:1092184

Guidry, Mike W ^[1]; Billings, J. J. ^[2]; Hix, William Raphael ^[1]

---

1. ORNL
2. Oak Ridge National Laboratory (ORNL)

In two preceding papers [1,2] we have shown that, when reaction networks are well removed from equilibrium, explicit asymptotic and quasi-steady-state approximations can give algebraically stabilized integration schemes that rival standard implicit methods in accuracy and speed for extremely stiff systems. However, we also showed that these explicit methods remain accurate but are no longer competitive in speed as the network approaches equilibrium. In this paper we analyze this failure and show that it is associated with the presence of fast equilibration timescales that neither asymptotic nor quasi-steady-state approximations are able to remove efficiently from the numerical integration. Based on this understanding, we develop a partial equilibrium method to deal effectively with the new partial equilibrium methods, give an integration scheme that plausibly can deal with the stiffest networks, even in the approach to equilibrium, with accuracy and speed competitive with that of implicit methods. Thus we demonstrate that algebraically stabilized explicit methods may offer alternatives to implicit integration of even extremely stiff systems, and that these methods may permit integration of much larger networks than have been feasible previously in a variety of fields.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1092184
• Journal Information: Computational Science & Discovery, Vol. 6, Issue 1; ISSN 1749--4699
• Country of Publication: United States
• Language: English