16,810 research outputs found
Direct Numerical Simulations
To understand and model the turbulent behavior of flowing fluids is one of the most fascinating, intriguing, annoying, and most important problems of engineering and physics. Admittedly most of the fluid flows are turbulent. In the known universe, turbulence is evident at the macroscopic scale and the microscopic scale in identical proportions. Turbulence is manifested in many places, such as: a plethora of technological devices, atmospheres and ocean currents, astronomical or galactic motions, and biological systems like circulation or respiration. With the continuum as an assumption, the equations that define the physics of fluid flow are the Navier-Stokes equations modeled during the mid-19th Century by Claude-Louis Navier and Sir George Gabriel Stokes. These equations define all flows, even turbulent flows, yet there is no analytical solution to even the simplest turbulent flow possible. However, the numerical solution of the Navier-Stokes equation is able to describe the flow variable as a function of space and time. It is called direct numerical simulations (DNS), which is the subject matter of this book
Direct numerical simulations of capillary wave turbulence
This work presents Direct Numerical Simulations of capillary wave turbulence
solving the full 3D Navier Stokes equations of a two-phase flow. When the
interface is locally forced at large scales, a statistical stationary state
appears after few forcing periods. Smaller wave scales are generated by
nonlinear interactions, and the wave height spectrum is found to obey a power
law in both wave number and frequency in good agreement with weak turbulence
theory. By estimating the mean energy flux from the dissipated power, the
Kolmogorov-Zakharov constant is evaluated and found to be compatible with the
exact theoretical value. The time scale separation between linear, nonlinear
interaction and dissipative times is also observed. These numerical results
confirm the validity of weak turbulence approach to quantify out-of equilibrium
wave statistics.Comment: Physical Review Letters (2014) in pres
Direct numerical simulations of aeolian sand ripples
Aeolian sand beds exhibit regular patterns of ripples resulting from the
interaction between topography and sediment transport. Their characteristics
have been so far related to reptation transport caused by the impacts on the
ground of grains entrained by the wind into saltation. By means of direct
numerical simulations of grains interacting with a wind flow, we show that the
instability turns out to be driven by resonant grain trajectories, whose length
is close to a ripple wavelength and whose splash leads to a mass displacement
towards the ripple crests. The pattern selection results from a compromise
between this destabilizing mechanism and a diffusive downslope transport which
stabilizes small wavelengths. The initial wavelength is set by the ratio of the
sediment flux and the erosion/deposition rate, a ratio which increases linearly
with the wind velocity. We show that this scaling law, in agreement with
experiments, originates from an interfacial layer separating the saltation zone
from the static sand bed, where momentum transfers are dominated by mid-air
collisions. Finally, we provide quantitative support for the use the
propagation of these ripples as a proxy for remote measurements of sediment
transport.Comment: 21 pages, 12 figure
Optimal Taylor-Couette flow: direct numerical simulations
We numerically simulate turbulent Taylor-Couette flow for independently
rotating inner and outer cylinders, focusing on the analogy with turbulent
Rayleigh-B\'enard flow. Reynolds numbers of and
of the inner and outer cylinders, respectively, are
reached, corresponding to Taylor numbers Ta up to . Effective scaling
laws for the torque and other system responses are found. Recent experiments
with the Twente turbulent Taylor-Couette () setup and with a similar
facility in Maryland at very high Reynolds numbers have revealed an optimum
transport at a certain non-zero rotation rate ratio
of about . For large enough in the numerically
accessible range we also find such an optimum transport at non-zero
counter-rotation. The position of this maximum is found to shift with the
driving, reaching a maximum of for . An
explanation for this shift is elucidated, consistent with the experimental
result that becomes approximately independent of the driving strength
for large enough Reynolds numbers. We furthermore numerically calculate the
angular velocity profiles and visualize the different flow structures for the
various regimes. By writing the equations in a frame co-rotating with the outer
cylinder a link is found between the local angular velocity profiles and the
global transport quantities.Comment: Under consideration for publication in JFM, 31 pages, 25 figure
Direct Numerical Simulations of Electrophoresis of Charged Colloids
We propose a numerical method to simulate electrohydrodynamic phenomena in
charged colloidal dispersions. This method enables us to compute the time
evolutions of colloidal particles, ions, and host fluids simultaneously by
solving Newton, advection-diffusion, and Navier--Stokes equations so that the
electrohydrodynamic couplings can be fully taken into account. The
electrophoretic mobilities of charged spherical particles are calculated in
several situations. The comparisons with approximation theories show
quantitative agreements for dilute dispersions without any empirical
parameters, however, our simulation predicts notable deviations in the case of
dense dispersions.Comment: 4pages, 3figures, to appear in Phys. Rev. Let
Direct numerical simulations of vortex rings at ReΓ = 7500
We present direct numerical simulations of the turbulent decay of vortex rings with ReΓ = 7500. We analyse the vortex dynamics during the nonlinear stage of the instability along with the structure of the vortex wake during the turbulent stage. These simulations enable the quantification of vorticity dynamics and their correlation with structures from dye visualization and the observations of circulation decay that have been reported in related experimental works. Movies are available with the online version of the paper
Direct Numerical Simulations of the Navier-Stokes Alpha Model
We explore the utility of the recently proposed alpha equations in providing
a subgrid model for fluid turbulence. Our principal results are comparisons of
direct numerical simulations of fluid turbulence using several values of the
parameter alpha, including the limiting case where the Navier-Stokes equations
are recovered. Our studies show that the large scale features, including
statistics and structures, are preserved by the alpha models, even at coarser
resolutions where the fine scales are not fully resolved. We also describe the
differences that appear in simulations. We provide a summary of the principal
features of the alpha equations, and offer some explanation of the
effectiveness of these equations used as a subgrid model for three-dimensional
fluid turbulence
Dipole Collapse and Dynamo Waves in Global Direct Numerical Simulations
Magnetic fields of low-mass stars and planets are thought to originate from
self-excited dynamo action in their convective interiors. Observations reveal a
variety of field topologies ranging from large-scale, axial dipole to more
structured magnetic fields. In this article, we investigate more than 70
three-dimensional, self-consistent dynamo models obtained by direct numerical
simulations. The control parameters, the aspect ratio and the mechanical
boundary conditions have been varied to build up this sample of models. Both,
strongly dipolar and multipolar models have been obtained. We show that these
dynamo regimes can in general be distinguished by the ratio of a typical
convective length scale to the Rossby radius. Models with a predominantly
dipolar magnetic field were obtained, if the convective length scale is at
least an order of magnitude larger than the Rossby radius. Moreover, we
highlight the role of the strong shear associated with the geostrophic zonal
flow for models with stress-free boundary conditions. In this case, the above
transition disappears and is replaced by a region of bistability for which
dipolar and multipolar dynamos co-exist. We interpret our results in terms of
dynamo eigenmodes using the so-called test-field method. We can thus show that
models in the dipolar regime are characterized by an isolated 'single mode'.
Competing overtones become significant as the boundary to multipolar dynamos is
approached. We discuss how these findings relate to previous models and to
observations.Comment: 35 pages, 16 figure
High performance Python for direct numerical simulations of turbulent flows
Direct Numerical Simulations (DNS) of the Navier Stokes equations is an
invaluable research tool in fluid dynamics. Still, there are few publicly
available research codes and, due to the heavy number crunching implied,
available codes are usually written in low-level languages such as C/C++ or
Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS
code that nearly matches the performance of C++ for thousands of processors and
billions of unknowns. We also describe a version optimized through Cython, that
is found to match the speed of C++. The solvers are written from scratch in
Python, both the mesh, the MPI domain decomposition, and the temporal
integrators. The solvers have been verified and benchmarked on the Shaheen
supercomputer at the KAUST supercomputing laboratory, and we are able to show
very good scaling up to several thousand cores.
A very important part of the implementation is the mesh decomposition (we
implement both slab and pencil decompositions) and 3D parallel Fast Fourier
Transforms (FFT). The mesh decomposition and FFT routines have been implemented
in Python using serial FFT routines (either NumPy, pyFFTW or any other serial
FFT module), NumPy array manipulations and with MPI communications handled by
MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT
in Python for a slab mesh decomposition using 4 lines of compact Python code,
for which the parallel performance on Shaheen is found to be slightly better
than similar routines provided through the FFTW library. For a pencil mesh
decomposition 7 lines of code is required to execute a transform
Direct Numerical Simulations of turbulent flow in a driven cavity
Direct numerical simulations (DNS) of 2 and 3D turbulent flows in a lid-driven cavity have been performed. DNS are numerical solutions of the unsteady (here: incompressible) Navier-Stokes equations that compute the evolution of all dynamically significant scales of motion. In view of the large computing resources needed for DNS cost-effective and accurate numerical methods are to be selected. Here, various-order accurate spatial discretization methods for DNS have been evaluated by applying them to the 2D driven cavity at Re = 22,000. To analyze the results of the DNS of the 2D flow in a driven cavity at Re = 22,000 the proper orthogonal decomposition (POD) technique has been applied. POD is an unbiased method to determine coherent structures. The Galerkin projection of the Navier-Stokes equations on the space spanned by the POD-basis-functions yields a relatively low-dimensional set of ordinary differential equations that mimics the dynamics of the Navier-Stokes equations. 3D DNS with no-slip conditions at all walls of the cavity have been performed at both Re = 3,200 and Re = 10,000. The results reproduce the experimentally observed Taylor-Görtler-like vortices.
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