8 research outputs found
Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes
In this paper we investigate the impact of the floating-point precision and
interpolation scheme on the results of direct numerical simulations (DNS) of
turbulence by pseudo-spectral codes. Three different types of floating-point
precision configurations show no differences in the statistical results. This
implies that single precision computations allow for increased Reynolds numbers
due to the reduced amount of memory needed. The interpolation scheme for
obtaining velocity values at particle positions has a noticeable impact on the
Lagrangian acceleration statistics. A tri-cubic scheme results in a slightly
broader acceleration probability density function than a tri-linear scheme.
Furthermore the scaling behavior obtained by the cubic interpolation scheme
exhibits a tendency towards a slightly increased degree of intermittency
compared to the linear one.Comment: to appear in Comp. Phys. Com
Two hierarchies of spline interpolations. Practical algorithms for multivariate higher order splines
A systematic construction of higher order splines using two hierarchies of
polynomials is presented. Explicit instructions on how to implement one of
these hierarchies are given. The results are limited to interpolations on
regular, rectangular grids, but an approach to other types of grids is also
discussed
Lagrangian Structure Functions in Turbulence: A Quantitative Comparison between Experiment and Direct Numerical Simulation
A detailed comparison between data from experimental measurements and
numerical simulations of Lagrangian velocity structure functions in turbulence
is presented. By integrating information from experiments and numerics, a
quantitative understanding of the velocity scaling properties over a wide range
of time scales and Reynolds numbers is achieved. The local scaling properties
of the Lagrangian velocity increments for the experimental and numerical data
are in good quantitative agreement for all time lags. The degree of
intermittency changes when measured close to the Kolmogorov time scales or at
larger time lags. This study resolves apparent disagreements between experiment
and numerics.Comment: 13 RevTeX pages (2 columns) + 8 figures include
On the efficiency and accuracy of interpolation methods for spectral codes
In this paper a general theory for interpolation methods on a rectangular
grid is introduced. By the use of this theory an efficient B-spline based
interpolation method for spectral codes is presented. The theory links the
order of the interpolation method with its spectral properties. In this way
many properties like order of continuity, order of convergence and magnitude of
errors can be explained. Furthermore, a fast implementation of the
interpolation methods is given. We show that the B-spline based interpolation
method has several advantages compared to other methods. First, the order of
continuity of the interpolated field is higher than for other methods. Second,
only one FFT is needed whereas e.g. Hermite interpolation needs multiple FFTs
for computing the derivatives. Third, the interpolation error almost matches
the one of Hermite interpolation, a property not reached by other methods
investigated.Comment: 19 pages, 5 figure
Statistical steady state in turbulent droplet condensation
Motivated by systems in which droplets grow and shrink in a turbulence-driven
supersaturation field, we investigate the problem of turbulent condensation in
a general manner. Using direct numerical simulations we show that the turbulent
fluctuations of the supersaturation field offer different conditions for the
growth of droplets which evolve in time due to turbulent transport and mixing.
Based on that, we propose a Lagrangian stochastic model for condensation and
evaporation of small droplets in turbulent flows. It consists of a set of
stochastic integro-differential equations for the joint evolution of the
squared radius and the supersaturation along the droplet trajectories. The
model has two parameters fixed by the total amount of water and the
thermodynamic properties, as well as the Lagrangian integral timescale of the
turbulent supersaturation. The model reproduces very well the droplet size
distributions obtained from direct numerical simulations and their time
evolution. A noticeable result is that, after a stage where the squared radius
simply diffuses, the system converges exponentially fast to a statistical
steady state independent of the initial conditions. The main mechanism involved
in this convergence is a loss of memory induced by a significant number of
droplets undergoing a complete evaporation before growing again. The
statistical steady state is characterised by an exponential tail in the droplet
mass distribution. These results reconcile those of earlier numerical studies,
once these various regimes are considered.Comment: 24 pages, 12 figure