Chebyshev and Fourier Spectral Methods

Ruelle`s principle for turbulence leading to what is usually called the Sinai-Ruelle-Bowen (SRB) distribution is applied to the statistical mechanics of many particle systems in nonequilibrium stationary states. A specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid. This presents the first test of the principle on a many particle system far from equilibrium. A possible application to fluid mechanics is also discussed.

Dynamical Ensembles in Nonequilibrium Statistical Mechanics.

▪ Abstract We review the direct numerical simulation (DNS) of turbulent flows. We stress that DNS is a research tool, and not a brute-force solution to the Navier-Stokes equations for engineering problems. The wide range of scales in turbulent flows requires that care be taken in their numerical solution. We discuss related numerical issues such as boundary conditions and spatial and temporal discretization. Significant insight into turbulence physics has been gained from DNS of certain idealized flows that cannot be easily attained in the laboratory. We discuss some examples. Further, we illustrate the complementary nature of experiments and computations in turbulence research. Examples are provided where DNS data has been used to evaluate measurement accuracy. Finally, we consider how DNS has impacted turbulence modeling and provided further insight into the structure of turbulent boundary layers.

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DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research

Astrophysical magnetic fields and nonlinear dynamo theory

Fast Fourier Transform

ALTHOUGH well developed turbulence exhibits complex, chaotic spatial and temporal behaviour, there is much experimental evidence to suggest that a remarkable degree of coherence is also present1. It is known2 that correlations in small-scale turbulent motions show significant deviations from the gaussian statistics usually expected for large, randomly interacting systems. This phenomenon, known as intermittency, has long resisted analytical description because of the lack of a simple, universal characterization of turbulence structures3. Here we report numerical simulations which show that there are remarkably simple spatial structures associated with intermittent regions of vorticity. In particular, in contrast to the classical description of turbulence as an array of 'pancake'- or 'lasagne'-like eddies4, we find that high-amplitude vortex structures are tube-like and that they generate local velocity fields that spiral around them.

Intermittent vortex structures in homogeneous isotropic turbulence

This paper presents a review of recent results on homogeneous turbulence. We discuss results obtained by direct numerical simulation as well as phenomenological models for the interpretation and understanding of these flows. In particular, we show that homogeneous turbulence can be well described in terms of a weakly correlated, random background field that is generally consistent with the classical Kolmogorov theory of turbulence, and strongly correlated, highly localized structures, that are largely responsible for intermittency effects and deviations from Kolmogorov scaling. These results give a unified dynamical picture of turbulence that describes both the energetics and intermittency of homogeneous turbulence, and allows us to develop a quantitative model for the description of the statistics of turbulence at small scales.

Structure and dynamics of homogeneous turbulence: models and simulations

The dynamics of vortex structures in turbulence have been investigated statistically in pseudospectral numerical simulations of moderate Reynolds number turbulence. Coherent features of vortex stretching dynamics, as manifested in the alignment of the vorticity vector with a principal axis of the rate of strain, are investigated with an emphasis on their time development in turbulence decay from a random gaussian field. In addition, we have observed a tendency in developed turbulence for velocity vectors to lie in the plane formed by the two principal stretching directions. These phenomena provide a mechanism for depletion of nonlinearity in turbulence. The spatial and temporal coherence of vortex structures has been further studied using recently developed techniques which combine dynamical visualisation with statistical sampling analysis.

Vortex structure and dynamics in turbulence

Coherent features of vortex structure and dynamics are investigated statistically in pseudo-spectral numerical simulations of moderate Reynolds number turbulence. The alignment of the vorticity vector with a principal axis of the rate of strain is investigated with an emphasis on its time development in turbulence decay from a random gaussian field. In addition, a tendency in developed turbulence for velocity vectors to lie in a plane formed by the two principal stretching directions is reported, leading to an explanation of depletion of nonlinearity in turbulence. The spatial and temporal coherence of vortex structures is further studied using recently developed techniques which combine dynamical visualization with statistical sampling analysis.

Statistical Aspects of Vortex Dynamics in Turbulence

We present results of a verification study of totally automated optical proximity correction (OPC) for mask redesign to enhance process capability. OPC was performed on an aggressive 0.35 micrometer i-line LSI logic SRAM design using the automated OPC generation code Eoptimask, employing the aerial image simulation code FAIM, both from Vector Technologies, Inc. Three different tests were performed, varying in the aggressiveness and type of corrections made. The key issues addressed in this work are the predictive capability of the aerial image simulation and, particularly, the ability of automatically generated OPC to significantly improve the fidelity of the final printed resist image for different geometries. The results of our study clearly demonstrate the utility of automated OPC based on aerial image simulation. Key experimental results include: two-fold increase of depth of focus latitude; demonstration of the feasibility of full off-axis illumination on the stepper; successful resolution of different feature types (posts, lines and spaces) on the wafer to correct CD at a single common exposure and focus condition. Future research will address detailed issues in reticle manufacture and inspection which are critical for cost-effective large-scale OPC.

Achieving sub-half-micron i-line manufacturability through automated OPC

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