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Turbulence Meets a Shock

XSEDE's Stampede2, ECSS Helps Simulate Shock Turbulence Interactions

A new theoretical framework was developed and tested using the Stampede2 supercomputer to understand turbulent jumps of mean thermodynamic quantities, shock structure and amplification factors. Turbulence comes in from the left in this image, hitting the shock, and leaving the domain from the right. This three-dimensional picture shows the structure of enstrophy and colored by local Mach number with the shock at gray. Credit: Chang-Hsin Chen, TAMU.


This may come as a shock, if you're moving fast enough. The shock being shock waves. A balloon's 'pop' is an example of shock waves generated by exploded bits of the balloon moving faster than the speed of sound. A supersonic plane generates a much louder sonic 'boom,' also from shock waves.

Farther out into the cosmos, a collapsing star generates shock waves from particles racing near the speed of light as the star goes supernova. Scientists are using supercomputers allocated through XSEDE to get a better understanding of turbulent flows that interact with shock waves. This understanding could help develop supersonic and hypersonic aircraft, more efficient engine ignition, as well as probe the mysteries of supernova explosions, star formation, and more.

"We proposed a number of new ways in which shock-turbulence interactions can be understood," said Diego Donzis, an associate professor in the Department of Aerospace Engineering at Texas A&M University. Donzis co-authored the study, "Shock–Turbulence Interactions at High Turbulence Intensities," published in May 2019 in the Journal of Fluid Mechanics. Donzis and colleagues used extremely high resolution simulations to support the team's novel theory of shockwaves in turbulence that accounts for features not captured by the seminal work on the subject.

Shock turbulence study co-authors Chang Hsin Chen (L) and Diego Donzis (R), pictured with the Stampede2 supercomputer. Drs. Chen and Donzis are both with the Department of Aerospace Engineering, Texas A&M University. Credit: TACC.

Enter Stampede2, an 18-petaflops supercomputer at the Texas Advanced Computing Center (TACC). Donzis was awarded compute time on Stampede2 through XSEDE. Both Stampede2 and XSEDE are funded by the National Science Foundation.

"On Stampede2, we ran a very large data set of shock-turbulence interactions at different conditions, especially at high turbulence intensity levels, with a degree of realism that is beyond what is typically found in the literature in terms of resolution at the small scales [and] in terms of the order of the scheme that we used," Donzis said. "Thanks to Stampede2, we can not only show how amplification factors scale, but also under what conditions we expect theory to hold, and under what conditions our previously proposed scaling is the more appropriate one."

Study lead author Chang Hsin Chen added, "We also looked at the structure of the shock and, through highly resolved simulations, we were able to understand how turbulence creates holes on the shock. This was only possible due to the computational power provided by Stampede2."

Another simulated view of turbulence coming from the left, hitting the shock, and leaving the domain from the right. The two-dimensional picture is Q-criterion and the shock is the thin blue line. Credit: Credit: Chang-Hsin Chen, TAMU.

Donzis furthered that "Stampede2 is allowing us to run simulations, some of them at unprecedented levels of realism, in particular the small-scale resolution that we need to study processes at the very small scales of turbulent flows. Some of these simulations run on half of the machine, or more, and sometimes they take months to run."

Making progress in understanding when turbulence meets shocks didn't come easy. Extreme resolution on the order of billions of grid points are needed to capture the sharp gradients of a shock in a high turbulent flow.

"While we are limited by how much we can push the parameter range on Stampede2 or any other computer for that matter, we have been able to cover a very large space in this parameter space, spanning parameter ranges beyond what has been done before," Donzis said. The input/output (I/O) also turned out to be challenging in writing the data to disk at very large core counts.

"This is one instance in which we took advantage of the Extended Collaborative Support Services (ECSS) from XSEDE, and we were able to successfully optimize our strategy," Donzis said. "We are now confident that we can keep increasing the size of our simulations with the new strategy and keep doing I/O at a reasonable computational expense."

Donzis is no stranger to XSEDE, which he's used for years back when it was called TeraGrid to develop his group's codes, starting with the LeMieux system at the Pittsburgh Supercomputing Center; Blue Horizon at the San Diego Supercomputer Center; Kraken at the National Institute for Computational Sciences; and now on Stampede1 and Stampede2 at TACC.

Better understanding of shock turbulence interactions could help develop supersonic and hypersonic aircraft, more efficient engine ignition, as well as probe the mysteries of supernova explosions, star formation, and more. NASA's Low-Boom Flight Demonstration supersonic aircraft illustrated here. Credit: NASA/Lockheed Martin.

"A number of the successes that we have today are because of the continued support of XSEDE, and TeraGrid, for the scientific community. The research we're capable of doing today and all the success stories are in part the result of the continuous commitment by the scientific community and funding agencies to sustain a cyberinfrastructure that allows us to tackle the greatest scientific and technological challenges we face and may face in the future. This is true not just for my group, but perhaps also for the rest of the scientific computing community in the U.S. I believe the XSEDE project and its predecessors in this sense have been a tremendous enabler," Donzis said.

The dominant theoretical framework for shock turbulence interactions, explained Donzis, goes back to the 1950s, developed by Herbert Ribner while at the University of Toronto, Ontario.  His work supported the understanding of turbulence and shocks interactions with a linear, inviscid theory, which assumes the shock to be a true discontinuity. The entire problem can thus be reduced to something mathematically tractable, where the results depend only on the shock's Mach number, the ratio of a body's speed to the speed of sound in the surrounding medium. As turbulence goes through the shock, it is typically amplified depending on the Mach number.

Experiments and simulations by Donzis and colleagues suggested ­this amplification depends on the Reynolds Number, a measure of how strong the turbulence is, and the turbulent Mach number, which is another parameter of the problem.

"We proposed a theory that combined all of these into a single parameter," Donzis said. "And when we proposed this theory a couple of years ago, we didn't have well-resolved data at very high resolution to test some of these ideas."

What's more, the scientists also explored shock jumps, which are abrupt changes in pressure and temperature as matter moves across a shock.

"In this study we developed and tested a new theoretical framework to understand, for example, why an otherwise stationary shock, starts moving when the incoming flow is turbulent," Donzis said. This implies that the incoming turbulence deeply alters the shock. The theory predicts, and the simulations on Stampede2 confirm, that the pressure jumps change, and how they do so when the incoming flow is turbulent. "This is an effect that is actually not accounted for in the seminal work by Ribner, but now we can understand it quantitatively," Donzis said.

Donzis is a firm believer that advances in HPC translate directly to benefits for all of society.

Said Donzis: "Advances in the understanding of shock turbulence interactions could lead to supersonic and hypersonic flight, to make them a reality for people to fly in a few hours from here to Europe; space exploration; and even our understanding of the structure of the observable universe. It could help answer, why are we here?  "

The study, "Shock–turbulence interactions at high turbulence intensities," was published in May 2019 in the Journal of Fluid Mechanics. The study authors are Chang Hsin Chen and Diego A. Donzis, Department of Aerospace Engineering, Texas A&M University. The study authors gratefully acknowledge support from the National Science Foundation (grant OCI-1054966) and the Air Force Office of Scientific Research (grants FA9550-12-1-0443, FA9550-17-1-0107).

Stampede1, Stampede2, and the Extended Collaborative Support Services program are allocated resources of the Extreme Science and Engineering Discovery Environment (XSEDE) funded by the National Science Foundation (NSF).