A team of researchers from the Okinawa Institute of Science and Technology (OIST) and the University of Turin, investigating how fast a fluid filled with particles mixes with a particle-free one, has solved what they described as the “100,000-body problem” using complex algorithms and advanced supercomputer clusters capable of simultaneously simulating hundreds of thousands of moving particles in a full three dimensions.
The team behind the new solution, which is playfully nicknamed for the infamous three-body problem, argues that their approach could improve wastewater treatment and chemical refining processes, and assist in developing strategies to combat seemingly unpredictable environmental incidents such as sinkholes and soil runoff.
“If the Three-Body Problem is Famously Complex, Imagine the 100,000-Body Problem.”
Although calculating the motion of a single object is relatively straightforward, when systems involve more than two distinct objects, calculating their complex interplay has proven notoriously frustrating. In astrophysics, where scientists must calculate collective gravitational forces within a planetary system, the conundrum is famously known as the “three-body problem.”
Calculating the interplay of multiple objects at such small scales has proved equally challenging, including characterizing everyday phenomena such as the speed of falling raindrops or the rate of sediment settling in a river estuary. These elusive mathematical principles also govern the mixing of sedimentary material in rising smoke, the behavior of dust storms, the dynamics of nuclear explosions, and several other phenomena.
“Scientifically describing the mechanics of how individual grains of sand fall to the bottom of a river, or even the overall rate of mixing between sediment-filled and clear water, is made difficult by the immense complexity of the forces involved and the unpredictability of long-term interactions,” the researchers explain.
According to the OIST and University of Turin team, these questions all come down to understanding how fluids containing particles mix with particle-free ones. This includes characterizing the weight and volume displacement of each particle within the fluid, how each particle drags liquid along via friction, any external influences such as gravity or an acceleration field, and the overall effect each particle’s mere presence has on the others.
“If the three-body problem is famously complex, imagine the 100,000-body problem,” explained Simone Tandurella, a PhD student in the Complex Fluids and Flows Unit at OIST, and the first author of the study detailing the team’s research.
Simulating a Process “Thought Impossible to Render Computationally”
According to a statement announcing the ‘solution’ to the 100,000-body problem, the researchers note that they began by simulating the movement of 100,000 three-dimensional particles suspended in a fluid composed of hundreds of millions of distinct points. Before this effort, the team said that these many simultaneously interacting parameters were “until now thought impossible to render computationally.”
Tandurella said that this process involved calculating the forces that each solid particle exerts on the surrounding points within the fluid, and the forces the fluid exerts on the particle. After calculating these forces, the researcher said that the team would sum the forces for each individual particle, solve the fundamental Navier-Stokes equations of fluid motion throughout the grid, and then “move one step.”
“This is done over millions of steps,” Tandurella explained.
Given the complexity of the 100,000-body problem, the team employed highly specialized software they had developed over many years, which could handle the fluid modelling equation at scale. Tandurella also noted that solving these complex equations was only possible with the “unique architecture of the OIST supercomputing cluster.”
“Without either, it wouldn’t be possible,” the researcher explained.
Approach Yields Immediate Results
To test their solution, the researchers modelled sediment plume formation. According to supercomputer simulations, when suspended heavy particles in the fluid sink due to gravity, friction drags the fluid around them down as well. The team said that this “pulls along” any surrounding particles, which exert their own independent forces to move the fluid further. This previously incalculable dynamic results in the formation of sediment plumes.
“The plume displaces an equivalent volume of clear fluid, which rises at an equivalent rate and further pushes sediment-filled fluid down,” they explained.
The team’s solution to the 100,000-body problem also revealed another mechanism at work. Because a particle’s terminal velocity is relative to its surrounding fluid, the particles closest to the center of the forming plume “accelerate to ever faster speeds.” The result of this asymmetrical motion increases the overall mixing rate, further driving plume formations.
Professor Marco Rosti, head of the Complex Fluids and Flows Unit, noted that solving such phenomena “couldn’t have been observed” using previous simulations that neglected the full interactions between particles and fluid.
“This is the first time that we’ve been able to replicate and study these behaviors accurately,” Professor Rosti explained.
The ‘Basic Puzzle Pieces’ to Understanding Large Scale Fluid-Particle Instabilities
When discussing the potential impact of the simulations and the theoretical framework required to accurately describe phenomena such as sediment mixing velocity, the team said it would provide researchers in physics and related fields with “better access to a wide range of fundamental phenomena in physics and other fields.”
These include research into dynamic fluid systems such as wastewater treatment facilities or chemical refinery operations.
“Both the simulations and the model we obtain enable exciting research into a wide range of fundamental physics phenomena, as well as applied research in fluid engineering,” Tandurella explained. “They provide the basic puzzle pieces that can help us understand fluid-particle instabilities at large scales.”
The study “A new form of mixing in turbulent sedimentation” was published in Physical Review Letters.
Christopher Plain is a Science Fiction and Fantasy novelist and Head Science Writer at The Debrief. Follow and connect with him on X, learn about his books at plainfiction.com, or email him directly at christopher@thedebrief.org.