Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box

Chiam, Keng-Hwee; Lai, Ming-Chih; Greenside, Henry

doi:10.1103/physreve.68.026705

Cited by 4 publications

(7 citation statements)

References 41 publications

(61 reference statements)

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“…If the domain were larger (Γ 40) the dynamics would be that of spiral defect chaos (c.f. [35]). For the domain we explore here, there are complex interactions between the bulk dynamics, which occurs several roll depths away and greater from the sidewalls, with dynamics that are strongly influenced by the sidewalls.…”

Section: Resultsmentioning

confidence: 99%

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Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

Paul

2016

Phys. Rev. E

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We explore numerically the high-dimensional spatiotemporal chaos of Rayleigh-Bénard convection using covariant Lyapunov vectors. We integrate the three-dimensional and time-dependent Boussinesq equations for a convection layer in a shallow square box geometry with an aspect ratio of 16 for very long times and for a range of Rayleigh numbers. We simultaneously integrate many copies of the tangent space equations in order to compute the covariant Lyapunov vectors. The dynamics explored has fractal dimensions of 20≲D_{λ}≲50, and we compute on the order of 150 covariant Lyapunov vectors. We use the covariant Lyapunov vectors to quantify the degree of hyperbolicity of the dynamics and the degree of Oseledets splitting and to explore the temporal and spatial dynamics of the Lyapunov vectors. Our results indicate that the chaotic dynamics of Rayleigh-Bénard convection is nonhyperbolic for all of the Rayleigh numbers we have explored. Our results yield that the entire spectrum of covariant Lyapunov vectors that we have computed are tangled as indicated by near tangencies with neighboring vectors. A closer look at the spatiotemporal features of the Lyapunov vectors suggests contributions from structures at two different length scales with differing amounts of localization.

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Section: Resultsmentioning

confidence: 99%

“…Our general approach for integrating Eqs. (1)-(3) is based upon the finite-difference algorithm developed by Chiam et al [35] to explore convection problems [36]. In our calculations we simultaneously integrate Eqs.…”

Section: Approachmentioning

confidence: 99%

Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

Paul

2016

Phys. Rev. E

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“…Both schemes were used to obtain the results presented in this article and were found to give good agreement with each other. Details of both of these schemes are available elsewhere [35,36]. For applications of these schemes to related problems in Rayleigh-Bénard convection, see Refs.…”

Section: B Direct Numerical Simulationsmentioning

confidence: 99%

Mean flow and spiral defect chaos in Rayleigh-Bénard convection

et al. 2003

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We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. First, we show that, in the absence of the mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wave numbers that approach those uniquely selected by focus-type singularities, which, in the absence of the mean flow, lie at the zigzag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how the mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of the mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with the Rayleigh number.

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“…For our calculations we have numerically integrated two copies of Eqs. (1)-(3) (one copy for each convection layer) that include the unidirectional coupling from the subdomain to the target domain using the approach de-scribed by Chiam et al [19] (see also [20]). We have used a uniform spatial resolution of ∆ = 1/8 and a time step of ∆t = 0.001.…”

Section: Resultsmentioning

confidence: 99%

Length scale of a chaotic element in Rayleigh-Bénard convection

Karimi

Paul²

2012

Phys. Rev. E

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We describe an approach to quantify the length scale of a chaotic element of a Rayleigh-Bénard convection layer exhibiting spatiotemporal chaos. The length scale of a chaotic element is determined by simultaneously evolving the dynamics of two convection layers with a unidirectional coupling that involves only the time-varying values of the fluid velocity and temperature on the lateral boundaries of the domain. In our results we numerically simulate the full Boussinesq equations for the precise conditions of experiment. By varying the size of the boundary used for the coupling we identify a length scale that describes the size of a chaotic element. The length scale of the chaotic element is of the same order of magnitude, and exhibits similar trends, as the natural chaotic length scale that is based upon the fractal dimension.

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Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box

Cited by 4 publications

References 41 publications

Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

Covariant Lyapunov vectors of chaotic Rayleigh-Bénard convection

Mean flow and spiral defect chaos in Rayleigh-Bénard convection

Length scale of a chaotic element in Rayleigh-Bénard convection

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