Qualitative modeling of the dynamics of detonations with losses

Abstract

We consider a simplified model for the dynamics of one-dimensional detonations with generic losses. It consists of a single partial differential equation that reproduces, at a qualitative level, the essential properties of unsteady detonation waves, including pulsating and chaotic solutions. In particular, we investigate the effects of shock curvature and friction losses on detonation dynamics. To calculate steady-state solutions, a novel approach to solving the detonation eigenvalue problem is introduced that avoids the well-known numerical difficulties associated with the presence of a sonic point. By using unsteady numerical simulations of the simplified model, we also explore the nonlinear stability of steady-state or quasi-steady solutions.

Influence of discrete sources on detonation propagation in a Burgers equation analog system

“…This approach has been expanded to study non-ideal one-dimensional detonations and was able to capture the instabilities caused by the presence of a loss term that can represent the effects of front curvature or friction on the detonation wave. [25] All of these prior studies treated the medium as being spatially uniform. The present paper is the first to examine discrete-source detonations in analogs based upon the Burgers equation.…”

The Clawpack 5.x software

“…Recent applications of PyClaw include studies of laser light trapping by moving refractive index perturbations [42], instabilities of weakly nonlinear detonation waves [13], and effective dispersion of nonlinear waves via diffraction in periodic materials [28]. Two of these are depicted in Figure 6.…”

“…PyClaw, these routines -including the Riemann solver itself -are selected at run-time, rather than at compile-time. These routines can be written directly in Python, or (if they are performance-critical) in a [13]. Right: Dispersion of waves in a layered medium with matched impedance and periodically-varying sound speed; see [28].…”

Peer Review #2 of "Clawpack: building an open source ecosystem for solving hyperbolic PDEs (v0.2)"

“…Recent applications of PyClaw include studies of laser light trapping by moving refractive index perturbations [51], instabilities of weakly nonlinear detonation waves [17], and effective dispersion of nonlinear waves via diffraction in periodic materials [33]. Two of these are depicted in Fig.…”

“…For instance, the computation shown in the right part of Fig. 8 involved more Figure 8: Left: A two-dimensional detonation wave solution of the reactive Euler equations, showing transverse shocks that arise from instabilities; see [17]. Right: Dispersion of waves in a layered medium with matched impedance and periodically-varying sound speed; see [33].…”