| TURBULENCE CHALLENGES
SHOCKLET SCIENCE
COMPUTING COMPRESSIBLE
TURBULENCE
 hockwaves
like the loud "boom" following an explosion or the sonic boom
of a supersonic aircraft are thin regions in a fluid across which
pressure and density rise rapidly. When a shockwave abruptly accelerates
an interface separating two different gases, this interface becomes
unstable, so that tiny disturbances grow over time, ultimately
leading to compressible turbulent mixing at the interface. Caltech
researcher Ravi Samtaney and colleagues are using powerful supercomputers
to model this kind of compressible turbulence more realistically
than ever before, providing tools to study the details of phenomena
from explosions to supernovae. This research is part of the Department of
Energy (DOE) sponsored Academic Strategic Alliances Program in
the Accelerated Strategic Computing Initiative (ASCI), begun to
conduct increasingly realistic testing in the virtual world that
cannot be done in the real world. The basic studies that Samtaney,
a senior research associate at Caltech, and colleagues Professor
Dale Pullin and researcher Branko Kosovic of Caltech are conducting
can be applied to modeling a range of applications. For example,
in order for astronomers to better understand nebulae and supernovae
(Figure 1), they need greater insight into shockwave dynamics.
Samtaney's studies can also be of use in the fusion research known
as Inertial Confinement Fusion (ICF), one possible approach to
meeting the world's growing energy needs, as well as in supersonic
combustion and other areas. Top
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TURBULENCE CHALLENGES
In studying turbulent flows, all important,
real-world cases are beyond the reach of exact solutions, even
with today's most powerful computers. This is due to the vast
range of scales in turbulence-from near the overall size of the
flow down to the very short scales where viscous forces dominate.
Moreover, there are vigorous and nonlinear interactions across
this wide range of scales. Thus, although researchers are principally
interested in predicting the overall flow dynamics, they cannot
ignore the influence of the smaller scales. To overcome the difficulty of resolving the
wide range of scales in turbulent motions, especially in real-world
applications, techniques such as Large-Eddy Simulations (LES)
are employed that include the larger-scale eddies but omit the
smaller scales, which "fall through the cracks" of the simulation
grids. "The challenge we face is to develop valid subgrid models
that will capture the dynamics of the flow that are smaller than
the resolution of the grid we can compute with, yet still reliably
predict how these small-scale dynamics will affect the larger
scale flow," said Samtaney. The researchers have developed a model of
the subgrid scale dynamics that they would like to apply to LES
studies of compressible turbulence, including the rapidly growing
Richtmyer-Meshkov instabilities on shockwave-accelerated interfaces
that play an important role in explosive flows. However, they
had to confirm that their model would work in decaying isotropic
turbulence, a difficult case for LES. To test their subgrid model, Samtaney and
colleagues used "experimental data" obtained from highly realistic
Direct Numerical Simulations (DNS) run on supercomputers, including
NPACI's Blue Horizon. Because these simulations solve the full
Navier-Stokes equations exactly, without approximations, and because
of the wealth of information they provide, such simulations are
increasingly used to gain insight into turbulent flows, and to
test models such as the researchers' subgrid turbulence model.
As a first step, Samtaney compiled a database
describing decaying isotropic turbulent flow within a cubic region
using high-resolution DNS runs with a mesh of 256 points on a
side, dividing the region into about 16 million cells and giving
a detailed picture of the turbulence. Such high-resolution simulations
are very computationally intensive, requiring long runs, even
on large supercomputers like Blue Horizon. Once the turbulence database had been compiled,
the next step was to test their subgrid model to see whether it
could reliably simulate turbulence in more complex cases. "To
do this, we put our subgrid turbulence model into the equations
for the turbulent flow, while running simulations at lower resolution,
a mesh of only 32 on a side," Samtaney said. This divides the
flow region into only about 32,000 cells, about 500 times less
than the full-size simulations. Because this coarse resolution
cannot directly resolve the smaller eddies, they must be accounted
for by the subgrid model, hence testing whether it can predict
the results from the exact, higher-resolution simulations. Samtaney found that the subgrid model satisfactorily
reproduced the overall, first-order results of the high-resolution
DNS simulations in the database. This has given the researchers
confidence that their subgrid model can be used in the larger
LES codes for simulating real-world flows, including Richtmyer-Meshkov
instabilities, in the ASCI Virtual Test Facility or astrophysics
simulations. Top
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Figure 2. Shocklets in Turbulent
Compressible Flow
Volume rendering of velocity
divergence in Direct Numerical Simulations of isotropic
decaying turbulence. The long, stringy structures indicate
shocklets or regions of large negative divergence, marking
zones of strong compression. Note the similarity to nebula
images (Figure 1). Such shockwaves are near-discontinuities
in the flow where the flow decelerates from supersonic to
subsonic across the shock front in a frame of reference
attached to the shock. The presence of shocklets is challenging
for computational models of compressible turbulent flows.
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"Our initial motivation was to develop a subgrid
model that would enable us to conduct larger simulations, but
when we did some simulations we saw that the velocity divergence
field had the broadband spectra characteristic of shock discontinuities,
that there were weak shocks in the flow-what we call shocklets,"
said Samtaney. The researchers also noticed that in astrophysical
cases (Figure 1) there are structures that looked strikingly similar
to the shocklet structures present in their simulations (Figure
2).
Having found shocklets in his exact DNS simulations,
Samtaney needed to be sure that his subgrid model would still
work in the presence of these shocklets. So the researchers started
looking into the dynamics of the shocklets, distilling the research
into the following question: "Given a box of turbulence at a given
Taylor Reynolds number and turbulent Mach number, can we estimate
the shocklet distribution?" In their large DNS simulations of isotropic
turbulence, the researchers were able to compute the statistical
characteristics of the flow, including the shocklets. And while
shocklets are present in the flow, it turns out that these structures
are not very dynamically significant. Samtaney explains that they
can be thought of as passive shocks that are being sloshed around
by the flow-these shockwaves can compress the gas, but because
they are relatively weak they have little effect on the overall
turbulent flow. "However, from a computational point of view,
their existence is a challenge because they are near-discontinuities
in the flow, and because we are using a nearly spectrally accurate
method, you start to get ringing," said Samtaney. Because this
numerical error can contaminate the results, the researchers had
to ensure that this did not happen. An interesting result of the DNS simulations
is that "we were able to achieve quite a lot in terms of quantifying
shocklets with a probability density function (PDF). In addition
to being able to demonstrate that our subgrid model is valid even
with shocklets, the essential result of this research is that
we were able to get a model for the PDF of the shocklet strength,
the statistics of shocklet occurrence, as a function of the Mach
number or the pressure ratio across the shock, and neither of
these has been done before," said Samtaney. The researchers also
developed an algorithm to extract shocklets from the DNS simulations,
finding stringy, "ribbon-like" surfaces (Figure 3). "A question people often ask is what is the
mechanism of generation of the shocklets," said Samtaney. One
plausible mechanism involves two vortices that are counter-rotating
so that the fluid flowing between them is accelerated, and when
accelerated supersonically it can decelerate only through a shock,
so the shocklets might be thought of as sitting in the throat
of two vortices," said Samtaney. While this is one possible mechanism
consistent with the elongated structure of shocklets, this area
has yet to be explored in detail. "Our overall goal was to see if our subgrid
turbulence model would work in the presence of shocks, at least
weak shocks, and we're pleased that it performs reasonably well,"
Samtaney said. Now the team is shifting its attention to using
the subgrid model in large-eddy simulations of larger, real-world
cases. Top
| Contents | Next COMPUTING COMPRESSIBLE
TURBULENCE
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Figure 3. Shocklet Extraction Algorithm
Results
Results of the algorithm developed
to extract the presence of shocklets or weak shockwaves
from the high-resolution Direct Numerical Simulations of
turbulence. Note the similarity in shape to the long, stringy
structures in Figure 2.
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In building their database of isotropic turbulence,
the researchers carried out DNS simulations in a cubic domain.
This approach resolves the full Navier-Stokes equations with no
models or approximations using a 10th-order accurate finite-difference
code. Samtaney explains that it is a compact finite difference
code that can be thought of as being spatially implicit, that
is, each step forward in time involves the velocities and other
quantities over the whole space. The researchers used a high resolution 256
cubed grid, dividing the region into some 32 million cells. Running
on 128 processors of Blue Horizon, the runs typically took seven
to 10 days, some 50 to 80 hours. "We had to run lots of diagnostics
and that took a lot of time. We computed the DNS and the statistics
on the fly, and stored the entire solution every 1 to 1.5 large
eddy turnover time, saving the results in the HPSS here at caltech
and at SDSC as well," Samtaney said. A further benefit is that the DNS database
of isotropic turbulence is a resource that can be used by other
researchers to investigate various aspects of turbulence including
verifying LES models. Because of the usefulness of the database
and the large amount of work and computer time required to compile
it, the researchers are making this database of turbulence solutions
available so that others will not need to repeat this work. —PT
 Top
| Contents | Next www.galcit.caltech.edu/~ravi/compturb.html
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Project Leader
Dan Meiron
Caltech Participants
Ravi Samtaney,
Dale Pullin,
Branko Kosovic
Caltech |
SDSC - UC San Diego, MC 0505 |
9500 Gilman Drive |
La Jolla, CA 92093-0505
