Variable time-stepping exponential integrators for chemical reactors with analytical Jacobians

TL;DR

This paper introduces EPI3V, a variable time-stepping exponential integrator for stiff chemical combustion problems, demonstrating comparable or better performance than traditional implicit methods in several test cases.

Contribution

The paper presents a novel exponential integrator, EPI3V, tailored for stiff chemical kinetics, with analysis and comparison to implicit methods across multiple chemical mechanisms.

Findings

EPI3V performs similarly or better than BDF methods in most cases.

EPI3V converges even when performance degrades relative to implicit methods.

Performance analysis suggests potential improvements for exponential integrators.

Abstract

Computational chemical combustion problems are known to be stiff, and are typically solved with implicit time integration methods. A novel exponential time integrator, EPI3V, is introduced and applied to a spatially homogeneous isobaric reactive mixture. Three chemical mechanism of increasing complexity are considered, and in two cases the novel method can perform similar if not marginally better to a well-known implementation of a BDF implicit method. In one specific case we see relative performance degradation of the EPI3V to the implicit method. Despite this, the novel exponential method does converge for this case. A performance analysis of the exponential method is provided, demonstrating possible avenues for performance improvement.