Explicit Integration of Extremely-Stiff Reaction Networks: Asymptotic Methods

TL;DR

This paper demonstrates that explicit integration methods, stabilized by algebraic techniques, can effectively handle extremely stiff reaction networks, offering a competitive alternative to implicit methods especially for large systems.

Contribution

Introduction of asymptotic explicit methods tailored for extremely stiff, weakly equilibrated systems, with systematic evidence of their efficiency compared to implicit approaches.

Findings

Explicit methods can match implicit methods in accuracy and speed.

Stabilization depends on the system's proximity to equilibrium.

Explicit algorithms enable larger network integration than previously feasible.

Abstract

We show that, even for extremely stiff systems, explicit integration may compete in both accuracy and speed with implicit methods if algebraic methods are used to stabilize the numerical integration. The required stabilizing algebra depends on whether the system is well-removed from equilibrium or near equilibrium. This paper introduces a quantitative distinction between these two regimes and addresses the former case in depth, presenting explicit asymptotic methods appropriate when the system is extremely stiff but only weakly equilibrated. A second paper examines quasi-steady-state methods as an alternative to asymptotic methods in systems well away from equilibrium and a third paper extends these methods to equilibrium conditions in extremely stiff systems using partial equilibrium methods. All three papers present systematic evidence for timesteps competitive with implicit methods. Because an explicit method can execute a timestep faster than an implicit method, algebraically-stabilized explicit algorithms might permit integration of larger networks than have been feasible before in various disciplines.