Efficient numerical stability analysis of detonation waves in ZND

TL;DR

This paper introduces a new, potentially faster and more stable numerical algorithm for analyzing the linear stability of planar detonation waves, improving upon classical methods with modern Evans function techniques.

Contribution

The authors develop a novel algorithm based on Evans function theory that enhances stability analysis of detonation waves compared to traditional approaches.

Findings

The new algorithm is simpler and easier to implement.

It offers potential improvements in speed and numerical stability.

The method reexamines and modernizes classical stability analysis techniques.

Abstract

As described in the classic works of Lee--Stewart and Short--Stewart, the numerical evaluation of linear stability of planar detonation waves is a computationally intensive problem of considerable interest in applications. Reexamining this problem from a modern numerical Evans function point of view, we derive a new algorithm for their stability analysis, related to a much older method of Erpenbeck, that, while equally simple and easy to implement as the standard method introduced by Lee--Stewart, appears to be potentially faster and more stable.