2,588 research outputs found
Computational coarse graining of a randomly forced 1-D Burgers equation
We explore a computational approach to coarse graining the evolution of the
large-scale features of a randomly forced Burgers equation in one spatial
dimension. The long term evolution of the solution energy spectrum appears
self-similar in time. We demonstrate coarse projective integration and coarse
dynamic renormalization as tools that accelerate the extraction of macroscopic
information (integration in time, self-similar shapes, and nontrivial dynamic
exponents) from short bursts of appropriately initialized direct simulation.
These procedures solve numerically an effective evolution equation for the
energy spectrum without ever deriving this equation in closed form.Comment: 21 pages, 7 figure
Observations, theoretical ideas and modeling of turbulent flows: Past, present and future
Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement
Large eddy simulation of two-dimensional isotropic turbulence
Large eddy simulation (LES) of forced, homogeneous, isotropic,
two-dimensional (2D) turbulence in the energy transfer subrange is the subject
of this paper. A difficulty specific to this LES and its subgrid scale (SGS)
representation is in that the energy source resides in high wave number modes
excluded in simulations. Therefore, the SGS scheme in this case should assume
the function of the energy source. In addition, the controversial requirements
to ensure direct enstrophy transfer and inverse energy transfer make the
conventional scheme of positive and dissipative eddy viscosity inapplicable to
2D turbulence. It is shown that these requirements can be reconciled by
utilizing a two-parametric viscosity introduced by Kraichnan (1976) that
accounts for the energy and enstrophy exchange between the resolved and subgrid
scale modes in a way consistent with the dynamics of 2D turbulence; it is
negative on large scales, positive on small scales and complies with the basic
conservation laws for energy and enstrophy. Different implementations of the
two-parametric viscosity for LES of 2D turbulence were considered. It was found
that if kept constant, this viscosity results in unstable numerical scheme.
Therefore, another scheme was advanced in which the two-parametric viscosity
depends on the flow field. In addition, to extend simulations beyond the limits
imposed by the finiteness of computational domain, a large scale drag was
introduced. The resulting LES exhibited remarkable and fast convergence to the
solution obtained in the preceding direct numerical simulations (DNS) by
Chekhlov et al. (1994) while the flow parameters were in good agreement with
their DNS counterparts. Also, good agreement with the Kolmogorov theory was
found. This LES could be continued virtually indefinitely. Then, a simplifiedComment: 34 pages plain tex + 18 postscript figures separately, uses auxilary
djnlx.tex fil
The effect of Turbulence Models on Numerical Prediction of Air Flow within Street Canyons
November 15-17, Belgrad
Development of turbulence models for shear flows by a double expansion technique
Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent
Discussion of the potential and limitations of direct and large-eddy simulations
The full text of the discussion paper presented at the Whither Turbulence Workshop on the potential and limitations of direct and large-eddy simulations is provided. Particular emphasis is placed on discussing the role of numerics and mathematical theory in direct simulations of both compressible and incompressible flows. A variety of unresolved issues with large-eddy simulations such as their implementation in high-order finite difference codes, problems with defiltering, and modifications to accommodate integrations to solid boundaries are elaborated on. These as well as other points are discussed in detail along with the authors' views concerning the prospects for future research
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