72,067 research outputs found
Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations
The dynamic model for large-eddy simulation (LES) of turbulent flows requires
test filtering the resolved velocity fields in order to determine model
coefficients. However, test filtering is costly to perform in large-eddy
simulation of complex geometry flows, especially on unstructured grids. The
objective of this work is to develop and test an approximate but less costly
dynamic procedure which does not require test filtering. The proposed method is
based on Taylor series expansions of the resolved velocity fields. Accuracy is
governed by the derivative schemes used in the calculation and the number of
terms considered in the approximation to the test filtering operator. The
expansion is developed up to fourth order, and results are tested a priori
based on direct numerical simulation data of forced isotropic turbulence in the
context of the dynamic Smagorinsky model. The tests compare the dynamic
Smagorinsky coefficient obtained from filtering with those obtained from
application of the Taylor series expansion. They show that the expansion up to
second order provides a reasonable approximation to the true dynamic
coefficient (with errors on the order of about 5 % for c_s^2), but that
including higher-order terms does not necessarily lead to improvements in the
results due to inherent limitations in accurately evaluating high-order
derivatives. A posteriori tests using the Taylor series approximation in LES of
forced isotropic turbulence and channel flow confirm that the Taylor series
approximation yields accurate results for the dynamic coefficient. Moreover,
the simulations are stable and yield accurate resolved velocity statistics.Comment: submitted to Theoretical and Computational Fluid Dynamics, 20 pages,
11 figure
Towards finite density QCD with Taylor expansions
Convergence properties of Taylor expansions of observables, which are also
used in lattice QCD calculations at non-zero chemical potential, are analyzed
in an effective N_f = 2+1 flavor Polyakov-quark-meson model. A recently
developed algorithmic technique allows the calculation of higher-order Taylor
expansion coefficients in functional approaches. This novel technique is for
the first time applied to an effective N_f = 2+1 flavor Polyakov-quark-meson
model and the findings are compared with the full model solution at finite
densities. The results are used to discuss prospects for locating the QCD phase
boundary and a possible critical endpoint in the phase diagram.Comment: 11 pages, 6 figures; minor clarifying changes, version to be
published in Phys. Lett.
Lensing Simulation and Power Spectrum Estimation for High Resolution CMB Polarization Maps
We present efficient algorithms for CMB lensing simulation and power spectrum
es- timation for flat-sky CMB polarization maps. We build a pure B-mode
estimator to remedy E to B leakage due to partial sky coverage. We show that
our estimators are unbiased, and consistent with the projected errors. We
demonstrate our algorithm using simulated observations of small sky patches
with realistic noise and weights for upcoming CMB polarization experiments.Comment: 11 pages, 6 figure
Analysis of stochastic time series in the presence of strong measurement noise
A new approach for the analysis of Langevin-type stochastic processes in the
presence of strong measurement noise is presented. For the case of Gaussian
distributed, exponentially correlated, measurement noise it is possible to
extract the strength and the correlation time of the noise as well as
polynomial approximations of the drift and diffusion functions from the
underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference
Trace formulas for stochastic evolution operators: Smooth conjugation method
The trace formula for the evolution operator associated with nonlinear
stochastic flows with weak additive noise is cast in the path integral
formalism. We integrate over the neighborhood of a given saddlepoint exactly by
means of a smooth conjugacy, a locally analytic nonlinear change of field
variables. The perturbative corrections are transfered to the corresponding
Jacobian, which we expand in terms of the conjugating function, rather than the
action used in defining the path integral. The new perturbative expansion which
follows by a recursive evaluation of derivatives appears more compact than the
standard Feynman diagram perturbation theory. The result is a stochastic analog
of the Gutzwiller trace formula with the ``hbar'' corrections computed an order
higher than what has so far been attainable in stochastic and
quantum-mechanical applications.Comment: 16 pages, 1 figure, New techniques and results for a problem we
considered in chao-dyn/980703
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