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

Dmitry Kabanov; Aslan R. Kasimov

doi:10.1063/1.5020558

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

Dmitry Kabanov, Aslan R. Kasimov

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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.

Original language	English (US)
Pages (from-to)	036103
Journal	Physics of Fluids
Volume	30
Issue number	3
DOIs	https://doi.org/10.1063/1.5020558
State	Published - Mar 20 2018

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. For computer time, this work used the resources of the Supercomputing Laboratory at KAUST. A.R.K. was also partially supported by the Russian Foundation for Basic Research (Grant No. #17-53-12018).

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10.1063/1.5020558

https://repository.kaust.edu.sa/bitstream/10754/626509/1/1.5020558.pdf

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title = "Linear stability analysis of detonations via numerical computation and dynamic mode decomposition",

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.",

author = "Dmitry Kabanov and Kasimov, {Aslan R.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially supported by the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. For computer time, this work used the resources of the Supercomputing Laboratory at KAUST. A.R.K. was also partially supported by the Russian Foundation for Basic Research (Grant No. #17-53-12018).",

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doi = "10.1063/1.5020558",

language = "English (US)",

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T1 - Linear stability analysis of detonations via numerical computation and dynamic mode decomposition

AU - Kabanov, Dmitry

AU - Kasimov, Aslan R.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially supported by the King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia. For computer time, this work used the resources of the Supercomputing Laboratory at KAUST. A.R.K. was also partially supported by the Russian Foundation for Basic Research (Grant No. #17-53-12018).

PY - 2018/3/20

Y1 - 2018/3/20

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10754/626509

UR - http://arxiv.org/abs/1712.03276v1

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JO - Physics of Fluids

JF - Physics of Fluids

IS - 3

ER -

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

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