Researchers use supercomputers for largest-ever turbulence simulations
of its kind
Date:
February 14, 2022
Source:
Gauss Centre for Supercomputing
Summary:
Despite being among the most researched topics on supercomputers,
a fundamental understanding of the effects of turbulent motion
on fluid flows still eludes scientists. A new approach aims to
change that.
FULL STORY ==========================================================================
From designing new airplane wings to better understanding how fuel sprays ignite in a combustion engine, researchers have long been interested in
better understanding how chaotic, turbulent motions impact fluid flows
under a variety of conditions. Despite decades of focused research on the topic, physicists still consider a fundamental understanding of turbulence statistics to be among the last major unsolved challenges in physics.
==========================================================================
Due to its complexity, researchers have come to rely on a combination of experiments, semi-empirical turbulence models, and computer simulation
to advance the field. Supercomputers have played an essential role in
advancing researchers' understanding of turbulence physics, but even
today's most computationally expensive approaches have limitations.
Recently, researchers at the Technical University of Darmstadt
(TU Darmstadt) led by Prof. Dr. Martin Oberlack and the Universitat Polite`cnica de Vale`ncia headed by Prof. Dr. Sergio Hoyas started
using a new approach for understanding turbulence, and with the help
of supercomputing resources at the Leibniz Supercomputing Centre (LRZ),
the team was able to calculate the largest turbulence simulation of its
kind. Specifically, the team generated turbulence statistics through
this large simulation of the Navier-Stokes equations, which provided
the critical data base for underpinning a new theory of turbulence.
"Turbulence is statistical, because of the random behaviour we observe," Oberlack said. "We believe Navier-Stokes equations do a very good job of describing it, and with it we are able to study the entire range of scales
down to the smallest scales, but that is also the problem -- all of these scales play a role in turbulent motion, so we have to resolve all of it
in simulations. The biggest problem is resolving the smallest turbulent
scales, which decrease inversely with Reynolds number (a number that
indicates how turbulent a fluid is moving, based on a ratio of velocity,
length scale, and viscosity). For airplanes like the Airbus A 380,
the Reynolds number is so large and thus the smallest turbulent scales
are so small that they cannot be represented even on the SuperMUC NG." Statistical averages show promise for closing an unending equation
loop In 2009, while visiting the University of Cambridge, Oberlack
had an epiphany - - while thinking about turbulence, he thought about
symmetry theory, a concept that forms the fundamental basis to all areas
of physics research. In essence, the concept of symmetry in mathematics demonstrates that equations can equal the same result even when being
done in different arrangements or operating conditions.
========================================================================== Oberlack realized that turbulence equations did, in fact, follow these
same rules. With this in mind, researchers could theoretically forego
using the extremely large, dense computational grids and measuring
equations within each grid box -- a common approach for turbulence
simulations -- and instead focus on defining accurate statistical mean
values for air pressure, speed, and other characteristics. The problem
is, by taking this averaging approach, researchers must "transform"
the Navier-Stokes equations, and these changes unleash a never-ending
chain of equations that even the world's fastest supercomputers would
never be able to solve.
The team realized that the goal needed to be finding another accurate
method that did not require such a computationally intensive grid full
of equations, and instead developed a "symmetry-based turbulence theory"
and solved the problem through mathematical analysis.
"When you think of computations and you see these nice pictures of flows
around airplanes or cars, you often see grids," Oberlack said. "What
people have done in the past is identify a volume element in each box
-- whether it is velocity, temperature, pressure, or the like -- so we
have local information about the physics. The "symmetry-based turbulence theory" now allows to drastically reduce this extreme necessary resolution
and at the same time it directly provides the sought-after mean values
such as the mean velocity and the variance." Using an almost 100-year-old mathematical turbulence law, the logarithmic law of the wall, the team
was able to focus on a simple geometric shape to test the symmetry
theory -- in this case, a flat surface. In this simplified shape, the
team's theory proved successful -- the researchers found that this law
served as a foundational solution for the first equation in the seemingly unending string of equations, and that it therefore served as the basis
from which all subsequent equations in the chain could be solved.
This is significant, as researchers studying turbulence often must find
a place to cut, or close, this infinite string of equations, introducing assumptions and potential inaccuracies into simulations. This is known
as the closure problem of turbulence, and its solution has long eluded physicists and other researchers trying to better understand turbulent
motion of fluids.
==========================================================================
Of course, just like other mathematical theories, the researchers had
to try and verify what they had found. To that end, the team needed
to do computationally expensive direct numerical simulations (DNS)
to compare its results with what most researchers consider the most
accurate method for simulating turbulence. That said, DNS simulations
for even simple geometries are only capable of running on world-leading computational resources, such as LRZ's SuperMUC-NG supercomputer, which Professor Oberlack's team has been using extensively for years.
"For us, we wanted to have the most reliable database for comparing
our symmetry theory to data that is possible at the time," Oberlack
said. "For that reason, we had no other choice than doing DNS, because
we didn't want to have any effect of empirical influence other than
the assumptions contained in the Navier-Stokes equations themselves."
The team found excellent agreement between the simulation results and its theories, demonstrating that its approach shows promise for helping fluid dynamics researchers solve the elusive closure problem of turbulence.
Closing in on a long-time goal Oberlack indicated that the team was highly motivated to use its theory in other contexts, and as supercomputing
resources continue to get faster, the team hopes to test this theory on
more complex geometries.
Oberlack mentioned that he appreciated the role that LRZ played in
the work.
Several team members have participated in LRZ training courses, and while
the team was overall very experienced using HPC resources, it got good, responsive support from LRZ user support staff. "It is really important
to actually have humans behind these machines that are dedicated to
helping users," he said.
========================================================================== Story Source: Materials provided by
Gauss_Centre_for_Supercomputing. Original written by Eric Gedenk. Note:
Content may be edited for style and length.
========================================================================== Journal Reference:
1. Martin Oberlack, Sergio Hoyas, Stefanie V. Kraheberger, Francisco
Alca'ntara-A'vila, Jonathan Laux. Turbulence Statistics of Arbitrary
Moments of Wall-Bounded Shear Flows: A Symmetry Approach. Physical
Review Letters, 2022; 128 (2) DOI: 10.1103/PhysRevLett.128.024502 ==========================================================================
Link to news story:
https://www.sciencedaily.com/releases/2022/02/220214204055.htm
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