Visualization and feature extraction in isotropic
Navier-Stokes turbulence
Victor M. Fernandez and Norman J. Zabusky,
Department of Mechanical and Aerospace Engineering and CAIP Center
Rutgers University, Piscataway, NJ 08855
Smitha Bhat and Deborah Silver
Department of Electrical and Computer Engineering and CAIP Center
Rutgers University, Piscataway, NJ 08855
Shi-Yi Chen
IBM T.J. Watson Research Center / Theoretical Division
and Center for Nonlinear Studies, Los Alamos National Laboratory,
Los Alamos, NM 87545
Table of contents
1. Introduction
2. Feature extraction
3. Implementation
4. Example on the turbulence field
5. Conclusions
6. Acknowledgements
7. References
Figures
Abstract
We present feature extraction and data reduction algorithms and
provide an insight in the types of problems that arise in dealing with
large datasets, obtained in Navier-Stokes turbulence simulations with a
512^3 mesh resolution. The developed tools are based on
thresholding, object segmentation and low order ellipsoidal
quantifications and are applied to the search of coherent vortex
structures associated with maxima events in the turbulence field. We
underline the importance of sharing tasks between the supercomputer
(CM5) and the workstation (SGI Onyx), where each machine may work more
efficiently at different stages of the data processing. We obtain
visualizations that show the structure of the dominant coherent
objects. The reduced representations employed make it possible to
examine different types of fields for possible correlations. The
quantification of the objects identified by the feature extraction
algorithms, should contribute to the building of models that consider
both coherent structures and the random background observed in
Navier-Stokes turbulence.
T.o.C.
The emphasis on detecting and characterizing large-scale structures in
flows has been one of the most important motivations to apply digital
image processing to flow visualization [1]. Much of the time
of the computational aerodynamicist or fluid dynamicist will be
devoted, in the future, to extracting and displaying the critical
features of the computed solution [2]. Two approaches to
extracting graphical information and flow visualization are currently
evolving [2]. In one approach the engineer works at a
graphics workstation and displays various portions of the flow field.
Because the 3D dataset is large, this requires a very powerful
graphics workstation. This interactivity has the advantage that one
can discover information that might not be anticipated. The other
approach is to program the supercomputer itself to analyze the
database. In both of these approaches, algorithms must be developed
to search out and display features such as shock waves, vortices, and
separation lines [2]. In the case of large 3D databases,
supercomputers are used not only to compute the solution, but to
search the flow field itself [2]. For unsteady flows
(where the data volume may not even fit in the supercomputer's
memory), analysis of the flow field and extraction of the information
for graphical display will have to be done ``on the fly'' as the
computation is proceeding, or as a laborious process from magnetic
tape [2]. Because of the needed interaction between
supercomputer and workstation, high speed communication between the
machines is critical [2].
Visualization is a key component in the process of obtaining
quantitative and mathematical understanding of the numerical models
investigated in CFD (Computational Fluid Dynamics) [3].
Visualization tools must be able to sharpen the intuition of the
engineer or scientist and also contribute to building quantitative and
mathematical models. The approach we take to visualization is to
present data in a form where measurement (quantification) of relevant
magnitudes is emphasized. This approach, called visiometrics
[4], consists of several steps [5]. The basic
steps are "identification, quantification and
understanding/mathematization". Although this process presents a
natural progression, in fact it is an iterative refinement procedure,
which at the end produces the appropriate mathematical formulation [5].
Identification involves feature extraction, which has been considered
and carried out in different contexts, not only to help in the process
of obtaining understanding. Feature extraction can be used as a
selective way to display data, which avoids the excessive, confusing
visual clutter, that arises when too much information is shown
[2,6]. Besides supporting the understanding process
and helping to avoid visual clutter, feature extraction may be a very
effective and natural way to deal with large datasets. Many existing
visualization systems make performance trade-offs that assume relative
small quantities of data (solution and grid fit in RAM) [7].
Unfortunately no current computer can hold some of the time dependent
CFD datasets (from 5 to 162 Gigabyte), that are currently being
produced [7]. The key points in dealing with these datasets
are: extraction of ``scientific data'' and use of a ``persistent
object database'' [7]. These objects usually correspond to
``coherent structures'' (localized objects, which persist over
``characteristic times'' [5]). Feature extraction is
accompanied by large reductions in storage requirements (0.3 - 6.7%
of solution size) [7]. The disadvantage is that the
possibility to examine the solution domain outside the extracted
domain is lost [7].
Feature extraction can be accomplished in different ways. Initially
it can be just a thresholding operation and extrema tracking
[8] . It can also be viewed as the process of obtaining
reduced representations (ellipsoidal or skeletal representation plus
vector lines released from selected release points) for the data
[9][10]. These reduced representations of different
variables can be used to point out causal connections between them
[3,11,9,10]. The reduced
representations correspond to ``identified objects'' in
the data. and can be used as tools for perusal, interpretation,
quantification, feature tracking [5] and also for
yuxtaposition, i.e., detailed and quantitative comparison of
experimental and/or computational images of similar or different
functions at the same or different times [12]. Other feature
extraction procedures include the use of streamlines connected through
nodes or critical points, which characterize global flow topology
[13,14]. These methods have been implemented as
interactive tools to extract meaning from datasets [6]. The
critical point approach has also been implemented as modules (TOPO
[15]) in the visualization environments (FAST [16]).
In the particular case of isotropic turbulence simulations, different
researchers have used a ``probe'' or ``window'' (fixed or Lagrangian)
for searching and obtaining the full time history of vortex tubes
[17,18]. Their object identification algorithm
consists of taking a local maximum in the field, and tracing the
skeleton of the vortex tube. Diagnostics include the tube's length,
curvature, length to diameter ratio and circulation
[19]. Algorithms for extracting ``events''
[20] have indicated that intermittent
regions may be major, if not dominant contributors to global
statistics in turbulence. In studies of vortex collapse and
reconnection, other researchers have used a ``diagnostics box'' which
surrounds regions of significant physical behavior, detected through
the searching of maxima events [21,12].
In this work we use object identification algorithms to search for the
dominant vortex structures in isotropic 3D turbulence. The data was
produced by Dr. Shiyi Chen [22] at Los Alamos National
Laboratory and has a spatial resolution of 512^3 grid points in a
uniform mesh (Fig. 1). We explore the use of both a
massive parallel computer (the CM5) and the Onyx workstation
communicating in the frame of CMAVS/AVS networks and the use of simple
feature extraction techniques (in batch mode on the CM5) and
interactive postprocessing on the workstation. The examples reported
below were obtained on the CM5 (1024 nodes) and the SGI Onyx at the
Advanced Computing Laboratory at Los Alamos National Laboratory
(ACL-LANL) and the CM5 (512 nodes) at the National Center for
Supercomputing Applications (NCSA) and the SGI Onyx at the VIZLAB in
Rutgers. Our work addresses the need to distribute tasks among a
network of computers. We recognize that the solver, the solutions and
extractors should reside and operate on supercomputers, to be able to
deal with the main difficulty, which is the size of the dataset. For a
$512^3$ simulation, the volume of the dataset is of the order of 0.5
Gigabyte for a scalar field (single precision). In this mode of
operation, we need to be able to send different amounts of data across
the network for displaying or additional postprocessing in a
workstation.
Fig. 1 Turbulence 512^3 dataset. The vorticity
magnitude field shown in this figure is represented by spheres
corresponding to a set of thresholded points (20% of the maximum and
above).
T.o.C.
In this work we combine a feature extraction-object identification
algorithm to perform a guided search for vortex structures in the
turbulence field. The feature extraction is performed in three steps:
* thresholding
* object identification
* ellipsoid fitting
The objects in the dataset, or field, are defined by a scalar
function, $f( \bbox{x} )$, e.g. vorticity magnitude, and a threshold,
$f_{th}$. The first stage, thresholding, consist in finding and
extracting the points in the dataset where $f$ is above the threshold
specified by the user, including their position in space. For uniform
grids, the storage required for the position of the points corresponds
to a scalar value only, since it is possible to establish a map between
the 3D coordinates and a 1D value. The thresholding stage usually
allows a considerable reduction in the volume of information. In
Fig. 2 can be observed, that the number of grid points
with low vorticity magnitude values is very large. For this data set,
the amount of reduction obtained by selecting the points above the
threshold 20% of the maximum is from ~500 Megabyte (0.5
Gigabyte, original dataset) to ~15 Megabyte.
Object identification is performed on the thresholded grid points. The
approach we take is: starting with a grid point, we find all of the
points that are connected to it by checking their distances to the
starting point. The new detected points are then examined to find the
grid points that are connected to them. Every time a point is found to
be part of an object, this point is marked to eliminate it from the
subsequent search for the other objects. The algorithm is not
efficient because for every grid point the connectivity search
involves $O( N )$ pairwise operations, where $N$ is number of grid
points (i. e., the required operations is $O( N^2 )$). Because of the
large data reduction obtained by the thresholding process, this direct
method still can be carried out on the workstation. In the other hand,
the process could be done more efficiently on the parallel machine,
where the pairwise operations can be computed and checked
simultaneously.
Once the objects have been found, an object measurement
(quantification) process starts, which we call the ellipsoid fitting.
This is also a data reduction process that produces abstract
representations of the objects: the ellipsoids. This process consists
in finding the ``mass'', the centroid, the average orientation of the
vector field, the tensor of second moments, the maximum and the
position of the maximum inside each object $V_{ob}$ [3].
The reduced quantities $m, \bar{\bbox{x}}, \hat{\bbox{v}},
\nu_{ij}, f_{max}$ and $\bbox{x}_{max}$ are used to produce the
reduced representation of the objects: the ellipsoids. the tensor of
second moments $\nu_{ij}$. The position of the ellipsoids is the
centroid of the objects they represent. The axes of the ellipsoids are
the square root of the eigenvalues of the tensor of second moments
$\nu_{ij}$, normalized, so that the ellipsoids and the objects have
the same volume. The ellipsoids are oriented according to the
eigenvectors of the tensor $\nu_{ij}$. The reduced representation
obtained in this manner not only fits the shape of the object, but
averages over the values of the scalar field in the interior, making
it possible to differentiate between objects of similar shape and
volume. Taking one of the reduced quantities (usually $f_{max}$), the
objects are sorted and listed for further use by the user or other
postprocessing programs. The use of ellipses and ellipsoids and/or
the related tensor of second moments for visualization and diagnostics
has been diverse in the past. The method of moments has been applied
to pattern recognition problems, where characterization of images
through low-order moments is equivalent to using ellipses (in 2D)
[23]. Other application in image processing consisted in
finding the orientation of projections of 3D objects [24].
Ellipsoids have also been used as an iconic representation of 3D
tensor fields [25]. In the context of quantification,
ellipses were applied as a low-order momental model for the evolution
of well separated vortices [26]. Second order moments
were also used as diagnostics for the evolution of vortex patches
[27].
Fig. 2 Vorticity histogram of the isotropic
turbulence $512^3$ dataset. The horizontal axis is the vorticity
magnitude. The vertical axis is the number of grid points in each
of the vorticity magnitude bins, normalized.
T.o.C.
As a starting point for implementing these tools, we selected AVS
[28]. AVS is a commercial package widely
available, which is based on a dataflow model for visualization and
control [29]. AVS is constructed based on the modularity
and networking concept. Application units, called modules, are
organized and made available to the user through a ``network editor''.
The modules are selected by the user to form networks in the network
editor working area. The networks are therefore flexible enough to
meet the particular needs of the users. The modular characteristics of
AVS have the advantage that the user can produce his/her own modules
and insert them in networks of standard AVS modules, which makes
available to the user, all of the power of the commercial product, in
the user's very specific applications (the user doesn't need to
rewrite the whole package again). The other advantage is that AVS has
a mechanism to share tasks among different machines via ``remote
modules''. In particular there is available CMAVS, which is the
particular set of AVS modules for the CM5. Therefore, CMAVS/AVS
provides a framework for interaction between the supercomputer and the
workstation.
We tried to apply the feature extraction-object identification
algorithms in two different environments. In the first one we used a
remote CMAVS module running on the CM5 to send interactively selected
subdomains of a large dataset, trough the network, to AVS running on a
workstation, for displaying. The main motivation of this approach is
to use the memory available in the supercomputer to hold the required
amount of data, which can be hardly handled by the workstation. In the
second implementation, the large dataset is subjected to a
thresholding postprocessing operation (selective data reduction), in
the supercomputer, in batch mode. The resulting reduced dataset can
then be postprocessed interactively on the workstation. The reduced
dataset still covers the complete domain and allows to obtain a global
picture of the dataset.
3.1 Object segmentation
In order to deal with the large number of vortex structures present in
the turbulence dataset, we classify them according to their
relationship to maxima events, not only of vorticity magnitude but
strain-rate as well. One of the tools developed with this objective is
the ``object-segment'' program, which is an enhancement to the
standard iso-surfacing technique,used to extract coherent structures
from 3D datasets. After defining connectivity between datapoints, points
above a predefined threshold are grouped into a set of objects. Currently,
there are two versions of the object-segment program: the sequential
version and the parallel version on the CM5 (which supports up to 256
cubed datasets).
On the CM5, a number of parallel functions are used to represent the
datapoints and for operations of connectivity and membership. We
demonstrate the use of this feature isolation code in Fig. 3.
In this figure, the threshold value 20% of the maximum was used to
detect the objects observed, however, regions are extracted based upon
their connectivity. The dataset is a 256 cubed scalar field (vorticity
magnitude). The output of the program consist of a list of objects
sorted and colored according to the local maxima inside them, which
allows the user to select "coherent" regions for further
quantification. In the figure, after the objects in the field have
been identified, the predominant object (colored in red) is extracted
for closer examination (Fig. 3).
Fig. 3 The object-segment code separates
the objects found at a given threshold. The classification of the
objects is shown in the figure by coloring them according to the local
vorticity magnitude maxima inside each object. The program allows the user
to select single objects for further quantification.
The sequential version of the object-segment program handles both
regular and curvilinear datasets. For curvilinear datasets, the
periodic option has been added as for certain datasets, if an object
happens to extend along a boundary, it would be split into two objects
if periodicity is not enforced. For e.g, in the tokamak dataset,
points on the periodic boundary can have neighbours across the
boundary i.e. like a wrapping around. However in this case, the
mapping function between the physical and the computational space is
to be provided along with the dataset. In Fig. 4, the
use of the feature isolation code on curvilinear datasets is
demonstrated.
Fig. 4 Object-segmentation of a
curvilinear tokamak dataset (dimensions 32 x 129 x 65). Again, a single
object is selected for further quantification.
3.2 CMAVS and the interactive window in the large dataset
The large dataset produced on the
supercomputer, can be accessed more easily when it still resides there.
In particular, for the CM5, parallel I/O can be used if the dataset
resides in the SDA (Scalable Disk Array), which provides a capacity of
25-200 Gigabytes that can be accessed at 33-254 Megabytes/second [30].
It is possible to use the CMAVS/AVS interface to
access interactively the CM5 resources through the workstation. This
is accomplished by using the remote modules, which run on the CM5 and
are connected in a network on AVS running on the workstation. The main
objective of the CMAVS module ``my_r_s_cm'' is to use the resources
of the CM5 to read the data (512^3 ~ 500 Megabyte or 256^3 ~ 67 Megabyte),
using parallel I/O and to hold it in its memory.
After this process has been accomplished, the data reduction process
is necessary to make it possible, to transfer the data through the
network. Some researchers have tried to extend the processing stage
on the CM5. The information passed through the network is therefore
the geometries used in the rendering by the workstation [29].
The same authors have also tried to produce the
rendering (the 2D pixel map) on the CM5, which may have a smaller
volume of data, than the actual geometric objects forming an isosurface
(for example). In our case, the data reduction process we choose
consist in extracting an interactively selected cubic subdomain. This
subdomain is transferred as an AVS field trough the network to the
workstation, where the standard local modules can be used for
displaying (e.g. isosurface) Figs. 5 and 6.
The first dial in the module my_r_s_cm (Fig. 5)
allow the user to change the size of the extracted subdomain. The
other three dials permit to change the position of the extracted
subdomain, so that the user can browse through the data
(Fig. 6). The my_r_s_cm CMAVS module can be used to
view the whole dataset by adjusting the corresponding dial and using
the standard CMAVS module ``downsize'', which produces a reduced
dataset by decimation.
It is possible to work in this mode interactively using the whole CM5
(1024 nodes at ACL-LANL), as in fact has been done by some researchers
in special circumstances (ACL Mosaic home page). Nevertheless, in
practical situations, it is hard to obtain more than 128 nodes to work
interactively. At the NCSA CM5, the usual amount of resources allowed
for CMAVS modules are 32 nodes for 2.5min.
Another important factor for interactivity, is the amount spent in
transferring data between the CM5 and the workstation. For a subdomain
of $64^3$, we find that the amount of transfer time on a local
ethernet network between the CM5 and the Onyx machine (at ACL-LANL)
is very acceptable. The same case running on the CM5 at NCSA
(Illinois) and the Vizlab Onyx machine (New Jersey), takes a few more
seconds, but is still acceptable. Researchers at ACL expect to be
able to send considerable larger amounts of data by using the HIPPI
network.
Fig. 5 (a) CMAVS/AVS network showing the use
of the remote module my_r_s_cm running on the CM5 (b) Data file browser
showing list of available files in the SDA on the CM5 and input
parameters of the remote module my_r_s_cm.
Fig. 6 Run of the CMAVS module:
The diagnostic box is sent across the network
(CM5-NCSA/Onyx-VIZLAB) with a 64^3 vorticity magnitude subdomain.
The reports on the execution of the remote CMAVS module my_r_s_cm
are also included.
3.3 Selective data reduction
The shape of the vorticity magnitude histogram (Fig. 2)
indicates that the volume of the data can be reduced considerably by a
thresholding operation, even at low thresholds. In this approach a
selective data reduction process is performed on the data (in batch
mode) on the CM5. The dataset is read from the SDA using a fortran
subroutine. Then, in another subroutine (written in cstar), the
dataset is mapped onto a 1D array, which can be used to map the 3D
coordinates of the grid points to a 1D value. This value is stored as
the coordinate of the grid point, from which later the 3D coordinates
can be recovered again. The thresholded points (points with a scalar
value greater or equal to the threshold) are marked an enumerated. The
(1D) enumeration will be stored later as the coordinate value of the
grid point. The array containing the enumeration is also used to
simultaneously transfer the thresholded points to the reduced array by
using left indexing (cstar). The threshold we select is 20% of the
maximum in the dataset. The output file of this program contains the
position in the 1D array and the scalar value of the thresholded
points. The reduced datasets obtained in this way can have vorticity
magnitude and strain rate magnitude. The thresholded points have the
appearance of a set of scatter points.
The reduced dataset is the input for an AVS network that is used to
search the dataset to find the relevant vortex structures in the
turbulence example. This is done mainly by the three (non-standard)
modules ``read_scat'' (input), ``scatter'' (feature extraction-object
identification) and ``smabox'' (diagnostics box). Non-standard data
types for dataflow between the modules are introduced to handle the
new formats of data (scatter points and objects lists) produced by the
data reduction and object identification processes. Rendering is
achieved using standard AVS modules (Fig. 7).
The modules operate as follows. After read_scat reads the dataset
with the thresholded points, the module scatter performs object
identification (see Sec. 2) according to (a new) threshold
given interactively (through a dial) by the user
(Fig. 7). The first output is a list of "interesting"
objects to be examined. The second output is ``ellipsoids''
representing the objects in the list, which are colored according to
the local maximum inside the object. The last output of this module is
an AVS geometry (``nubes'' button) representing the "filtered" or
"thresholded" $512^3$ domain, which consist of spheres with size and
color proportional to the magnitude of the scalar field for each of the
thresholded points (Fig. 1). A dial allows to adjust the
size of the spheres (Fig. 7).
The smabox module takes as input the thresholded points from
read_scat and the list of interesting objects produced by the scatter
module (Fig. 7). Once the user chooses from the list
of interesting objects, this module takes the thresholded points
available in the original reduced dataset and puts them back in a
(smaller than the original) grid, called the diagnostics box, which is
used to visualize the region containing the selected object, using
standard AVS tools, like isosurface. This last step is not efficient
because we get again the large undesired volume of data. In order to
improve this process, we require the development of specific tools for
the scatter point format of the reduced dataset. The position of the
diagnostics box can also be changed using dials
(Fig. 7) that specify the position of the center of
the box. The use of this network will be illustrated in Sec. 4.
The input of the scatter module can be selected using
a different field than the input of the smabox module. In this way a
field can be visualized (e.g. vorticity magnitude) according to the
important objects found in a related field (e.g. strain rate
magnitude)
3.4 Tools for closer examination of selected regions
The previous network is used for searching the field. Once an
interesting region has been selected, an entire set of scalar, vector
and tensor fields can be extracted from the original large dataset,
covering only the interesting subdomain ($128^3$ can be handled easily
by the Onyx, but for the scale of the objects in the example provided,
$64^3$ or $48^3$ is better for closer examination). These smaller
datasets can be examined again using the feature extraction-object
identification algorithm of section 2. Now with the
purpose of using the ellipsoids as pointers to local maxima, which can
be also used as release points for vector line tracers. The module
``ellipsoids'' has as input a 3D scalar field. The output are fitted
ellipsoids and a list of objects (Fig. 8). The list
of objects is the input to the ``vtracer'' module, together with the
corresponding 3D vector field. This module traces vector lines
released from the interactively selected objects. The length of the
lines and the integration step can also be selected interactively
(Fig. 8).
Fig. 7 (a) AVS network showing the postprocessing of
the thresholded points dataset. (b) Modules produced to handle the
reduced dataset: read_sct, scatter and smabox, showing input parameters.
Fig. 8 (a) AVS network showing the use of the
ellipsoids as pointers and release regions for vector lines. (b)
Parameters of the ellipsoids and vtracer modules.
T.o.C.
Fig. 1 illustrates the output of the scatter module
consisting of spheres for each of the thresholded points (20% of
maximum). The simple thresholding operation allows us to obtain a
representation of the $512^3$ dataset. The size and the color of the
spheres is assigned according to the scalar value at each grid point
(color not visible in the black and white picture). A close up of
this representation is shown in Fig. 9.
Fig. 10 shows the diagnostic box. After putting the
thresholded points back on the 3D grid, it is possible to use the
standard AVS isosurface (Fig. 10). The ellipsoids
produced by the scatter module are used to guide the search for
relevant vortex structures in Fig. 11. In
this figure, only the objects with non-zero volume, i.e., the
objects with eigenvalues larger than one grid size, have the ellipsoid
representation. All of the other smaller objects are represented by
lines with length proportional to the eigenvectors. The list of
objects, represented by the ellipsoids, is used by the user to perform
a search of coherent structures by moving the diagnostics box
(Fig. 11) throughout the domain. The translation of the
diagnostics box is based on the position of the identified objects,
which the user can select using the classification of the objects
obtained according to their local maxima (which can be vorticity
magnitude, dissipation, vorticity/strain-rate alignment, etc). These
reduced representations, defined by the eigenvalues and eigenvectors
of the tensor of second moments of the points forming the objects, are
a low order representation of the scalar field. The ellipsoids give a
sense of average and orientation of the segmented regions.
The region containing the maximum vorticity magnitude is examined in
Fig. 12. The vorticity magnitude isosurface at the
threshold 30% of the maximum, shows the topology of this region. The
ellipsoids, fitted at the threshold 45% of the maximum mark the local
maxima regions inside the objects. The vector lines trace the
vorticity field inside the objects. Sets of bundles are released from
the three ellipsoids. The lines in the object in the tube at the
center of the picture seems to be formed by two parallel tubes winding
around each other, which bifurcate in the upper right corner region.
The isosurface in the lower pictures corresponds to the magnitude of
the strain-rate. It can be observed that the strain-rate maxima are
not localized in the same position as vorticity maxima, which has been
observed in other turbulence simulations [31]. Another view
of the same region is presented in Fig. 13. In
Fig. 14, we present vorticity and strain-rate magnitude
fields for the object classified as the 12th according to the
vorticity magnitude in the $512^3$ dataset. The vorticity in the two
parallel vortex tubes is of opposite sign, nevertheless it doesn't
seem to correspond to a case of collapse.
Fig. 9 The spheres
representation is used to visualize the vorticity
magnitude field inside the diagnostics box.
Fig. 10 After the diagnostics box
(in this case 200^3) is produced, standard AVS modules, like
isosurface in this figure, can be used.
Fig. 11 Use of the list of identified objects:
The list of identified
objects, represented by the ellipsoids (scatter module) is used to
guide the search of relevant vortex structures using the diagnostics
box (smabox module).
Fig. 12 First view of
the maximum vorticity magnitude object. The isosurface in the upper
figures represents the vorticity magnitude. In the lower figures, the
isosurface represents the strain-rate magnitude. The lines trace the
vorticity field and are released from the ellipsoids, which fit the
vorticity magnitude maxima regions.
Fig. 13 Second view of
the maximum vorticity magnitude object.
Fig. 14 View of the object 12, according to the classification
obtained by the scatter module.
T.o.C.
The work on feature extraction we have done, gave us a first insight
in the type of problems that arise when dealing with large datasets.
This first experience underlined the importance of sharing tasks
between the supercomputer and the workstation, where each machine may
work more efficiently at different stages of the processing of the
data. We have developed some tools to search the field for coherent
objects, but in order to get a better understanding of the processes
observed, new quantification tools are necessary. In particular we
need to find measures of the identified structures that will allow us
to describe them in a statistical manner. This measures should allow
us to determine if the structures we observe are generic. We expect
this approach will lead to a model that will consider both the
coherent structures observed and the random background in the
turbulence flow field.
An essential part of diagnostics corresponds to quantifications.
We have not been able to perform these in detail yet. In particular it
is important to determine if the vortex structures we observe are
generic. In order to investigate this question, it is necessary to
establish measures that will allow us to find how often this structures
appear in the field. Some of these techniques have been implemented in
other turbulence computations, where the radius, length and circulation
of the vortex tubes have been measured [19]. Also, it
is very important to follow the evolution in time of the detected
structures, to determine their dynamics. Some techniques developed
with these objectives have also been implemented before [17].
T.o.C.
Recent support was provided by DOE/ARPA. The computations were
performed on the CM5 at the Advanced Computing Laboratory-Los Alamos
National Laboratory and the CM5 at the National Center for
Supercomputing Applications.
T.o.C.
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