Optimization of One-parameter Family of Integration Formulae for Solving Stiff Chemical-kinetic ODEs

TL;DR

This paper introduces MACKS, a Jacobian-free, optimized one-parameter integration method for stiff chemical-kinetic ODEs, achieving higher accuracy and faster performance than previous methods like ERENA and VODE.

Contribution

The paper presents MACKS, a novel Jacobian-free integration approach that optimizes a family of formulae for improved accuracy and efficiency in solving stiff chemical-kinetic ODEs.

Findings

MACKS outperforms ERENA in accuracy.

MACKS enables faster homogeneous-ignition simulations than VODE.

The method is robust and suitable for stiff ODEs in chemical kinetics.

Abstract

A fast and robust Jacobian-free time-integration method - called Minimum-error Adaptation of a Chemical-Kinetic ODE Solver (MACKS) - for solving stiff ODEs pertaining to chemical-kinetics is proposed herein. The MACKS formulation is based on optimization of the one-parameter family of integration formulae coupled with a dual time-stepping method to facilitate error minimization. The proposed method demonstrates higher accuracy compared to the method - Extended Robustness-enhanced numerical algorithm (ERENA) - previously proposed by the authors. Additionally, when this method is employed in homogeneous-ignition simulations, it facilitates realization of faster performance compared to the Variable-coefficient ODE solver (VODE).