Instability and route to chaos in porous media convection

Research output: Contribution to journalReview article

2 Citations (Scopus)

Abstract

A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

Original languageEnglish (US)
Article number26
JournalFluids
Volume2
Issue number2
DOIs
StatePublished - Jun 1 2017

Fingerprint

Chaos theory
Porous materials
chaos
convection
routes
Boussinesq approximation
dependent variables
transition points
Ordinary differential equations
continuity
differential equations
Decomposition
decomposition
expansion
Convection
energy
Hot Temperature

Keywords

  • Chaos
  • Feedback control
  • Lorenz equations
  • Natural convection
  • Porous media
  • Weak turbulence

ASJC Scopus subject areas

  • Mechanical Engineering
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

Cite this

Instability and route to chaos in porous media convection. / Vadasz, Peter.

In: Fluids, Vol. 2, No. 2, 26, 01.06.2017.

Research output: Contribution to journalReview article

@article{16ae742ab12c4d099b6ce15efa7df076,
title = "Instability and route to chaos in porous media convection",
abstract = "A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.",
keywords = "Chaos, Feedback control, Lorenz equations, Natural convection, Porous media, Weak turbulence",
author = "Peter Vadasz",
year = "2017",
month = "6",
day = "1",
doi = "10.3390/fluids2020026",
language = "English (US)",
volume = "2",
journal = "Fluids",
issn = "2311-5521",
publisher = "Multidisciplinary Digital Publishing Institute",
number = "2",

}

TY - JOUR

T1 - Instability and route to chaos in porous media convection

AU - Vadasz, Peter

PY - 2017/6/1

Y1 - 2017/6/1

N2 - A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

AB - A review of the research on the instability of steady porous media convection leading to chaos, and the possibility of controlling the transition from steady convection to chaos is presented. The governing equations consisting of the continuity, the extended Darcy, and the energy equations subject to the assumption of local thermal equilibrium and the Boussinesq approximation are converted into a set of three nonlinear ordinary differential equations by assuming two-dimensional convection and expansion of the dependent variables into a truncated spectrum of modes. Analytical (weak nonlinear), computational (Adomian decomposition) as well as numerical (Runge-Kutta-Verner) solutions to the resulting set of equations are presented and compared to each other. The analytical solution for the transition point to chaos is identical to the computational and numerical solutions in the neighborhood of a convective fixed point and deviates from the accurate computational and numerical solutions as the initial conditions deviate from the neighborhood of a convective fixed point. The control of this transition is also discussed.

KW - Chaos

KW - Feedback control

KW - Lorenz equations

KW - Natural convection

KW - Porous media

KW - Weak turbulence

UR - http://www.scopus.com/inward/record.url?scp=85054331763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85054331763&partnerID=8YFLogxK

U2 - 10.3390/fluids2020026

DO - 10.3390/fluids2020026

M3 - Review article

VL - 2

JO - Fluids

JF - Fluids

SN - 2311-5521

IS - 2

M1 - 26

ER -