# Aslan KasimovSkolkovo Institute of Science and Technology | Skoltech

Aslan Kasimov

PhD

## About

63

Publications

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968

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Introduction

Additional affiliations

August 2009 - June 2016

August 2005 - August 2009

August 1999 - August 2005

## Publications

Publications (63)

We consider a one-dimensional gaseous detonation wave propagating in a channel with a spatially periodic friction factor with the purpose of understanding how non-uniform momentum losses affect the detonation dynamics. The problem is investigated by means of the shock-fitting numerical integration of reactive Euler equations. We examine in detail t...

We report on the phenomenon of detonation synchronization and demonstrate the existence of the Arnold tongues and devil's staircases in the problem of gaseous detonation in a periodically inhomogeneous reactive medium. Universal properties of these dynamical structures – the Farey tree, fractal dimension and period-doubling bifurcations – are revea...

In this work, we analyze numerically the dynamics of one-dimensional gaseous detonations propagating in a mixture with periodically varying properties such as density, temperature, or mixture composition. It is found that periodic upstream variations can lead to resonant amplification of intrinsic oscillations and to mode locking whereby the detona...

We perform high-resolution numerical simulations of three-dimensional dynamics of an elongated bubble in a microchannel at moderate Reynolds numbers up to 1800. For this purpose, we use the coupled Brinkman penalization and volume of fluid methods implemented in the open-source framework Basilisk. The new results are validated with available experi...

In this work, we contribute to the development of numerical algorithms for the direct simulation of three-dimensional incompressible multiphase flows in the presence of multiple fluids and solids. The volume of fluid method is used for interface tracking, and the Brinkman penalization method is used to treat solids; the latter is assumed to be perf...

Gaseous detonation propagation in a thin channel with regularly spaced cylindrical obstacles was investigated experimentally and numerically. The wave propagation with substantial velocity deficits is observed and the details of its propagation mechanism are described based on experimental measurements of the luminosity and pressure and on three-di...

In this work we analyze, within the framework of the reactive Burgers model (Kasimov et al., 2013), the propagation of detonation in a periodically varying medium. We investigate the role of the amplitude and the wavelength of the variations on the dynamics of both stable and unstable detonations. It is found that: (1) the periodic upstream can lea...

We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using...

We present a computational analysis of a 2×2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in the model is varied. Linear and nonlinear stability properties of the traveling waves are computed numerically using...

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...

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...

We propose a method to study linear stability of detonations by linearizing equations about steady-state, solving them numerically and then postprocessing using dynamic mode decomposition. We compare our results for the one-step model with the results obtained using normal-mode analysis. Besides, we show that our method is easily extensible to more...

We use numerical simulations of the reactive Euler equations to analyze the nonlinear stability of steady-state one-dimensional solutions for gaseous detonations in the presence of both momentum and heat losses. Our results point to a possible stabilization mechanism for the low velocity detonations in such systems. The mechanism stems from the exi...

The existence and structure of steady gaseous detonation propagating in a
packed bed of solid inert particles are analyzed in the one-dimensional
approximation by taking into consideration frictional and heat losses between
the gas and the particles. A new formulation of the governing equations is
introduced that eliminates the well-known difficult...

We extend the reactive Burgers equation presented in Kasimov et al. Phys.
Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to
include multidimensional effects. Furthermore, we explain how the model can be
rationally justified following the ideas of the asymptotic theory developed in
Faria et al. JFM (2015). The proposed model...

We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p n...

We report on the structure and dynamics of gaseous detonation stabilized in a supersonic flow emanating radially from a central source. The steady-state solutions are computed and their range of existence is investigated. Two-dimensional simulations are carried out in order to explore the stability of the steady-state solutions. It is found that bo...

We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p n...

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 curvat...

We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatia...

We consider a spatially explicit three-species food chain model, describing generalist top predator-specialist middle predator-prey dynamics. We investigate the long-time dynamics of the model and show the existence of a finite dimensional global attractor in the product space, L(2)(Ω). We perform linear stability analysis and show that the model e...

We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled by Cattaneo’s law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data toget...

We investigate the behavior of solutions of the complex Gross-Pitaevskii
equation, a model that describes the dynamics of pumped decaying Bose-Einstein
condensates. The stationary radially symmetric solutions of the equation are
studied and their linear stability with respect to two-dimensional
perturbations is analyzed. Using numerical continuatio...

Here we analyze properties of an equation that we previously proposed to
model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria,
and R. R. Rosales. Model for shock wave chaos. Physical Review Letters,
110(10):104104, 2013]. The equation is \[
u_{t}+\frac{1}{2}\left(u^{2}-uu\left(0_{-},t\right)\right)_{x}=f\left(x,u\left(0_{-},t...

We consider the Cauchy problem for the one-dimensional Timoshenko system coupled with heat conduction, wherein the latter is described by either the Cattaneo law or the Fourier law. We prove that heat dissipation alone is sufficient to stabilize the system in both cases, so that additional mechanical damping is unnecessary. However, the decay of so...

We propose the following model equation:
\[u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}), \] that predicts chaotic shock waves.
It is given on the half-line $x<0$ and the shock is located at $x=0$ for any
$t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ is assumed
to satisfy certain integrability constraints as explained in the main tex...

In this fluid dynamic video we present simulations of converging
two-dimensional detonation in a radially expanding supersonic flow of ideal
reactive gas. The detonation is found to be unstable and leads to formation of
characteristic cellular patterns. Without any obstacles in the flow, the
detonation keeps expanding radially. To retain the wave w...

Fundamental diagrams of vehicular traffic flow are generally multi-valued in
the congested flow regime. We show that such set-valued fundamental diagrams
can be constructed systematically from simple second order macroscopic traffic
models, such as the classical Payne-Whitham model or the inhomogeneous
Aw-Rascle-Zhang model. These second order mode...

We investigate the decay property of a Timoshenko system of thermoelasticity in the whole space for both Fourier and Cattaneo laws of heat conduction. We point out that although the paradox of infinite propagation speed inherent in the Fourier law is removed by changing to the Cattaneo law, the latter always leads to a solution with the decay prope...

Using the complex Gross-Pitaevskii equation (cGPE) with pumping and
decay terms that models the Bose-Einstein condensate of
exciton-polaritons, we numerically investigate the dynamics of
instability of its radially symmetric steady solutions. We develop
accurate algorithms for computing the steady state solution, the linear
stability spectra, as we...

When a vertical jet of fluid strikes a horizontal plate, a circular hydraulic jump is often observed. Despite its apparent simplicity, the hydraulic jump exhibits features which are still poorly understood, the most striking of which is the instability of the circular shape with the resultant formation of stationary or spinning polygonal jumps. Her...

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 results are shown to agree with the predictions of linear stability analysis. Comparisons are made with linear perturbation growth rates and oscillation fre...

We present a method of simulating one-dimensional axisymmetric detonations governed by the reactive Euler equations in a reference frame moving with the shock surface. We use this methodology to verify relations between normal detonation speed, Dn, and curvature, (kappa), as predicted by Detonation Shock Dynamics (DSD), an asymptotic theory derived...

"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a related class of self-sustained transonic waves, namely detonations. Through this analogy, we describe the jam structure; favorable agreement with reported measurements from...

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions to the hyperbolic (“inviscid”) continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes tra...

We propose a theory of a steady circular hydraulic jump based on the shallow-water model obtained from the depth-averaged Navier–Stokes equations. The flow structure both upstream and downstream of the jump is determined by considering the flow over a plate of finite radius. The radius of the jump is found using the far-field conditions together wi...

We propose a theory of a stationary circular hydraulic jump that is based on the shallow water equations and a careful treatment of the far-field boundary conditions. We show that a unique solution for the radius of the hydraulic jump is obtained by matching the jump conditions and the critical flow downstream of the jump. A gasdynamic analogue of...

We present an overview of the current state of detonation stability theory and discuss its implications for propulsion. The emphasis of the review is on the exact or asymptotic treatments of detonations, including various asymptotic limits that appear in the literature. The role that instability plays in practical detonation-based propulsion is of...

Based on a general theory of detonation waves with an embedded sonic locus that we have previously developed, we carry out asymptotic analysis of weakly curved slowly varying detonation waves and show that the theory predicts the phenomenon of detonation ignition and failure. The analysis is not restricted to near Chapman–Jouguet detonation speeds...

A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional...

We apply the theory of weakly curved and slowly varying detonations, that we have recently developed, to the problem of detonation initiation in explosives described by a general equation of state and single-step rate law. Application to spherically expanding gaseous detonations initiated by a strong point-blast wave shows that the theory successfu...

In this work we investigate the dynamics of self-sustained detonation waves that have an embedded information boundary such that the dynamics is influenced only by a finite region adjacent to the lead shock. We introduce the boundary of such a domain, which is shown to be the separatrix of the forward characteristic lines, as a generalization of th...

Printout. Thesis (Ph. D.)--University of Illinois at Urbana-Champaign, 2004. Vita. Includes bibliographical references (leaves 203-212).

We describe a rigorous mathematical treatment of detonation waves with embedded sonic locus. A derivation of the general compatibility condition in the characteristic surface for reactive Euler equations with multi-step chemistry and general equation of state is given. The condition so derived reduces in appropriate limits to the radiation conditio...

In this work we provide a general mathematical background for the analytical treatment of detonation waves with embedded sonic locus (CJ detonations). A derivation of the general compatibility condition in the characteristic surface for reactive Euler equations with multiple-step chemistry and general equation of state is given. The condition so de...

We investigate hydrodynamic instability of a steady planar detonation wave propagating in a circular tube to three-dimensional linear perturbations, using the normal
mode approach. Spinning instability is identified and its relevance to the well-known
spin detonation is discussed. The neutral stability curves in the plane of heat release
and act...

Combustion of solid fuel particles has many important applications, including power generation and space propulsion systems. The current models available for describing the combustion process of these particles, especially porous solid particles, include various simplifying approximations. One of the most limiting approximations is the lumping of t...

There is a definite inconsistency between the classical ZND theory of detonation and contemporary experimental observations and attempts to model real detonation waves. Nevertheless, the classical one-dimensional model of detonation is still extensively used in interpreting measurements because of its simplicity and physical clarity. This naturally...

There is a definite inconsistency between the classical ZND theory of detonation and contemporary experimental observations and attempts to model real detonation waves. Nevertheless, the classical onedimensional model of detonation is still extensively used in interpreting measurements because of its simplicity and physical clarity. This naturally...

Numerical simulation of detonation waves is a challenging problem due to resolution requirements necessary to compute highly nonlinear multiple-scale dynamics of the shock--reaction zone structure. Widely used shock-capturing techniques are often inadequate when dealing with unstable detonations. Large errors at the lead shock propagate into the re...

In this work we discuss the application of an evolution equation that we have developed for the dynamics of a slowly evolving weakly-curved detonation to a problem of direct detonation initiation. Despite the relative simplicity of the theory, it successfully explains basic features of the initiation process which are observed in experiments and nu...

## Projects

Project (1)

Study of linear stability of steady-state solutions for detonation models.
Considered models: reactive Euler equations with one- and two-step kinetics.