4,732 research outputs found
Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection
We study hexagon patterns in non-Boussinesq convection of a thin rotating
layer of water. For realistic parameters and boundary conditions we identify
various linear instabilities of the pattern. We focus on the dynamics arising
from an oscillatory side-band instability that leads to a spatially disordered
chaotic state characterized by oscillating (whirling) hexagons. Using
triangulation we obtain the distribution functions for the number of pentagonal
and heptagonal convection cells. In contrast to the results found for defect
chaos in the complex Ginzburg-Landau equation and in inclined-layer convection,
the distribution functions can show deviations from a squared Poisson
distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at
http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J.
Physic
The Spatio-Temporal Structure of Spiral-Defect Chaos
We present a study of the recently discovered spatially-extended chaotic
state known as spiral-defect chaos, which occurs in low-Prandtl-number,
large-aspect-ratio Rayleigh-Benard convection. We employ the modulus squared of
the space-time Fourier transform of time series of two-dimensional shadowgraph
images to construct the structure factor .
This analysis is used to characterize the average spatial and temporal scales
of the chaotic state. We find that the correlation length and time can be
described by power-law dependences on the reduced Rayleigh number .
These power laws have as yet no theoretical explanation.Comment: RevTex 38 pages with 13 figures. Due to their large size, some
figures are stored as separate gif images. The paper with included hi-res eps
figures (981kb compressed, 3.5Mb uncompressed) is available at
ftp://mobydick.physics.utoronto.ca/pub/MBCA96.tar.gz An mpeg movie and
samples of data are also available at
ftp://mobydick.physics.utoronto.ca/pub/. Paper submitted to Physica
DEFECT-DEFERRED CORRECTION METHOD FOR THE TWO-DOMAIN CONVECTION-DOMINATED CONVECTION-DIFFUSION PROBLEM
We present a method for solving a fluid-fluid interaction problem (two convection-dominated convection-diusion problems adjoined by an interface), which is a simplifed version of the atmosphere ocean coupling problem. The method resolves some of the issues that can be crucial to the fluid-fluid interaction problems: it is a partitioned time stepping method, yet it is of high order accuracy in both space and time (the two-step algorithm considered in this report provides second order accuracy); it allows for the usage of the legacy codes (which is a common requirement when resolving flows in complex geometries), yet it can be applied to the problems with very small viscosity/diffusion coefficients. This is achieved by combining the defect correction technique for increased spatial accuracy (and for resolving the issue of high convection-to-difusion ratio) with the deferred correction in time (which allows for the usage of the computationally attractive partitioned scheme, yet the time accuracy is increased beyond the usual result of partitioned methods being only first order accurate) into the defect-deferred correction method (DDC). The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is unconditionally stable and the accuracy in both space and time is improved after the correction step
Dual weighted residual based error control for nonstationary convection-dominated equations: potential or ballast?
Even though substantial progress has been made in the numerical approximation
of convection-dominated problems, its major challenges remain in the scope of
current research. In particular, parameter robust a posteriori error estimates
for quantities of physical interest and adaptive mesh refinement strategies
with proved convergence are still missing. Here, we study numerically the
potential of the Dual Weighted Residual (DWR) approach applied to stabilized
finite element methods to further enhance the quality of approximations. The
impact of a strict application of the DWR methodology is particularly focused
rather than the reduction of computational costs for solving the dual problem
by interpolation or localization.Comment: arXiv admin note: text overlap with arXiv:1803.1064
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