2010/11/06 by Blake Barker, Barker, Blake, Kevin Zumbrun +1
Engineering · Mathematics · #Combustion and Detonation Processes #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1011.1561
openalex publication_date 2010/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We carry out a systematic numerical stability analysis of ZND detonations of Majda's model with Arrhenius-type ignition function, a simplified model for reacting flow, as heat release and activation energy are varied. Our purpose is, first, to answer a question of Majda whether oscillatory instabilities can occur for high activation energies as in the full reacting Euler equations, and, second, to test the efficiency of various versions of a numerical eigenvalue-finding scheme suggested by Humpherys and Zumbrun against the standard method of Lee and Stewart. Our results suggest that instabilities do not occur for Majda's model with Arrhenius-type ignition function, nor with a modified Arrhenius-type ignition function suggested by Lyng--Zumbrun, even in the high-activation energy limit. We find that the algorithm of Humpherys--Zumbrun is in the context of Majda's model 100-1,000 times faster than the one described in the classical work of Lee and Stewart and 1-10 times faster than an optimized version of the Lee--Stewart algorithm using an adaptive-mesh ODE solver