Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

TL;DR

This paper presents a novel numerical method combining shock-fitting and dynamic mode decomposition to analyze the linear stability of gaseous detonations, providing an alternative to traditional normal-mode analysis.

Contribution

The authors develop and demonstrate a new approach for detonation stability analysis using numerical integration and dynamic mode decomposition, applicable to various kinetic models.

Findings

Stability spectra computed for different reaction kinetics.

The new method is a viable alternative to normal-mode analysis.

Successful application to both one-step and two-step reaction models.

Abstract

We introduce a new method to investigate linear stability of gaseous detonations that is based on an accurate shock-fitting numerical integration of the linearized reactive Euler equations with a subsequent analysis of the computed solution via the dynamic mode decomposition. The method is applied to the detonation models based on both the standard one-step Arrhenius kinetics and two-step exothermic-endothermic reaction kinetics. Stability spectra for all cases are computed and analyzed. The new approach is shown to be a viable alternative to the traditional normal-mode analysis used in detonation theory.