A minimal hyperbolic system for unstable shock waves

  title={A minimal hyperbolic system for unstable shock waves},
  author={Dmitry Kabanov and Aslan R. Kasimov},
  journal={Commun. Nonlinear Sci. Numer. Simul.},
5 Citations

Derivatives on the downstream side of a moving, curved shock

  • G. Emanuel
  • Physics
    Journal of Engineering Mathematics
  • 2019
Novel relations are developed for the tangential and normal derivatives of the pressure, density, and velocity components just downstream of a regular point on a curved shock wave. The perfect gas

Three-dimensional simulations of detonation propagation in circular tubes: Effects of jet initiation and wall reflection

In the present work, using a high-resolution three-dimensional numerical analysis, the initiation and propagation mechanism of a detonation wave is studied in a circular tube with a hot jet



Stability of the square-wave detonation in a model system

Nonlinear Dynamics of Shock and Detonation Waves in Gases

ABSTRACT A review of analytical studies for the formation of triple points on shock fronts and for the cellular structures of gaseous detonations is presented. The analyses concern two opposite

Nonlinear dynamics and chaos analysis of one-dimensional pulsating detonations

To understand the nonlinear dynamical behaviour of a one-dimensional pulsating detonation, results obtained from numerical simulations of the Euler equations with simple one-step Arrhenius kinetics

Theory of weakly nonlinear self-sustained detonations

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier–Stokes equations. We show that these equations can

Recent Results on Stability of Planar Detonations

We describe recent analytical and numerical results on stability and behavior of viscous and inviscid detonation waves obtained by dynamical systems/Evans function techniques like those used to study

Mode selection in weakly unstable two-dimensional detonations

A formulation of the reactive Euler equations in the shock-attached frame is used to study the two-dimensional instability of weakly unstable detonation through direct numerical simulation. The

Qualitative modeling of the dynamics of detonations with losses

Weakly Nonlinear Detonation Waves

The authors develop a simplified asymptotic model for studying nonlinear detonation waves in chemically reacting fluids which propagate with wave speed close to the acoustical sound speed. In this

Stability of viscous detonations for Majda’s model

Theory of Detonation with an Embedded Sonic Locus

This work addresses the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave by proposing to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations.