• Researchers use supercomputers for large

    From ScienceDaily@1:317/3 to All on Mon Feb 14 21:30:46 2022
    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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