hydrodynamic simulation

High-frequency sound focused on a single point acts like an invisible lens gathering sunlight. Inside a tumor, such a lens can raise the temperature to about 72°C in a second, like hot water from a tap, but inside living tissue. Meanwhile, surrounding healthy cells remain almost untouched.

The universe right after the Big Bang was like a boiling cauldron: bubbles of a new state of matter were bursting and growing everywhere. These were first-order phase transitions — exactly like water boiling, only at temperatures reaching trillions of degrees.

The early universe was less like a calm pond and more like a boiling cauldron. Matter flowed, collided, and swirled against the backdrop of rapid spatial expansion. To understand how stars and galaxies emerged from this hot soup, physicists build digital simulations. This new work is the third part in a series on lattice-based cosmological modeling. The first two focused on fields; this one deals with fluids.

A subway train races through a tunnel, yet passengers in the last car barely sway. Blood flow in the lungs works much the same way: the heart pumps blood in powerful spurts, but by the time it reaches the veins, the pulsation has almost vanished.

Deep space, galactic center. A supermassive black hole is surrounded by a scorching disk of gas and dust. And then, through this fiery veil, a star shoots by every few hours — like an arrow loosed from the bow of gravity. Each passage triggers a dazzling X-ray flare that for a moment outshines the entire galactic nucleus.

At the heart of almost every galaxy slumbers a supermassive black hole — the invisible conductor of a stellar orchestra. When galaxies collide, their central monsters draw closer, entwining in a gravitational dance. Sometimes a third partner joins the duo, and then a triple waltz begins, its outcome unpredictable.

In the first moments of its life, the Universe resembled a boiling cauldron. As it cooled, phase transitions occurred — much like steam turning into water, but instead of molecules, the very state of space changed. In this cauldron, bubbles of the new phase were born, akin to bubbles in a pot coming to a boil.

Air flowing over a wing or turbine blade behaves like a string: it starts smooth and layered: that's the laminar regime. But as speed increases or external ripples appear, the string breaks into chaotic vibration — turbulence. Predicting the exact moment of breakdown is crucial: it affects drag, heating, and noise.

Picture a pot of boiling soup, but every grain in it is not just a point but a tiny top spinning around its own axis. That's the world of spin-1 particles. For example, some short-lived mesons born in accelerator collisions.

A planet the size of Neptune, but glowing white-hot. Beneath the clouds lies an ocean of magma capable of absorbing an entire hydrogen atmosphere. The new SEAMIST model is the first to trace how such dissolution changes a planet's fate from birth to old age. The big surprise is the mechanism of catastrophic boiling.

In the heart of a molecular cloud, a massive star is born. Its ultraviolet light ionizes hydrogen, and the cloud flares in the Lyman-alpha line. But for the photon, this flare is not liberation but imprisonment in a hall of mirrors.

Astronomers build maps of galaxies and listen to the radio whisper of neutral hydrogen. The signal is so faint that even a working TV would drown it out, but sensitive antennas pick it up from the depths of the Universe.

An ordinary lightbulb glows brighter as it heats up — everyone knows that. But a black hole the size of an atomic nucleus follows different rules.

A clap of the hands compresses the air, and it flies outward — the simplest shock. In space, exploding stars play the role of hands: their shock waves sharply compress gas and trigger chaotic mixing — turbulence.

Mountain river water doesn't flow smoothly: it churns, swirls into eddies, and suddenly accelerates. This chaotic motion is called turbulence. But even within it, there are hidden rhythms — rare and intense bursts that briefly alter the entire flow pattern.

A drop of honey spreads slowly across a table, while water spreads quickly. The resistance to flow, viscosity, differs from one fluid to another. But what if the viscosity changes on the fly, as the substance compresses or expands?

A stellar river winds around the center of a distant galaxy like a glowing ribbon on an invisible frame. That frame is the dark halo: a vast cloud of invisible dark matter whose gravity holds stars and gas in place. If the halo is squashed like a pumpkin or stretched like a melon, the stellar stream will bend differently.

A boiling pot, a gust of wind, a wisp of smoke from a campfire — all obey equations that mathematicians call 'nonlinear and dissipative.' In plain terms, energy is lost to friction, and parts of the flow influence each other so strongly that predicting the motion ahead of time is a task on the edge of feasibility.

Water going down the drain swirls into a vortex. An everyday sight in the kitchen. But this very vortex turned out to be able to reproduce two effects that physicists usually associate with black holes and the rotation of planets. The first effect is the shift of a wave as it goes around an obstacle.

In a pot of boiling water, steam bubbles rise and pop. In the quantum world of a superfluid, bubbles behave differently: they can collide and give birth to vortices — tiny swirling flows, like whirlpools in a river. Scientists modeled such a liquid using a holographic approach.

The void can produce particles if a strong enough field is applied. Physicists call this the Dirac–Klein paradox. Previously, explaining it required the most complex calculations of quantum field theory. But we can make do with a visual image: a tightly stretched rubber band with a knot. The knot is a particle.

In a cloud, thousands of tiny water droplets hang in the air. For rain to fall, they need to grow: stick together into larger drops and become heavy enough to fall to the ground. But how exactly do droplets find each other in a huge cloud? Scientists created a computer model that tracks each droplet individually, as if each one had its own little sensor.

A gamma-ray burst is a brief but extremely powerful flash of light, born from the merger of neutron stars or the collapse of a massive star. Inside such a flash, plasma flows race at enormous speeds and collide with each other.

A tiny gold star melts under the beam of an electron microscope, its points slowly rounding off. In the past, such a process could only be seen in snapshots taken with long pauses, and the probing beam itself would alter the sample.

Water in a river flows around rocks, air bends around an airplane wing: these motions are described by equations that are hard to solve even on a powerful computer. Neural networks can approximate such solutions, but they often err when data is collected at only a few points or is noisy.

Superbubbles are cosmic giants, akin to soap bubbles, but instead of soap film, they contain rarefied interstellar gas, and they're inflated not by a breath but by a series of supernova explosions. In computer simulations, they behave like living things: they grow, cool, and move. But until now, we couldn't precisely trace their boundaries.

Plasma is a gas in which electrons are stripped from atoms, behaving like a soup of charged particles. To predict how such a soup flows and heats up, you need to know how particles collide and exchange energy.

E. coli is a tiny swimmer in a world where water is as thick as jelly. Inside our gut, it doesn't glide freely but fights through mucus — a tangled web of long molecules, like a ball of knotted threads.

A membrane for water electrolysis is like a sponge soaked with water. Inside it, hydroxide ions, particles that carry electric charge, must move freely. But exactly how they move has long been a mystery: tracking each ion in an experiment is too difficult.

In turbulent air, droplets don't fly in straight lines: they get tossed around like dust motes in a beam of light. Physicists have built a setup that tracks each droplet, which is about a tenth of the thickness of a human hair. A camera captures their motion, and a computer reconstructs their trajectories.

Every few years, the warm current off the coast of Peru shifts, and fishermen come home empty-handed. This is El Niño, the breath of the tropical Pacific, which affects weather from Indonesia to California. Predicting its arrival is as hard as predicting where a stone thrown into a raging river will roll.

The Sun regularly produces explosions that hurl huge clouds of charged particles into space. Such a cloud travels toward Earth and can knock out satellites, disrupt radio communications, and even leave cities without electricity.

In a dark, cold cloud between the stars, a dust grain a thousandth of a millimeter across catches light molecules. Carbon monoxide and hydrogen stick to its surface like raindrops to glass and react. After a few steps, methanol is produced — the same alcohol found in windshield washer fluid.

On October 1, 2024, a class X7.1 flare erupted on the Sun — one of the most powerful. Two spacecraft, HXI and STIX, watched it from different angles, like two eyes, and together with a computer model helped reconstruct the three-dimensional picture.

If you force water through a narrow neck, the flow speeds up right at the edge, and a whirlpool forms behind the obstacle. Electrons in ultra-clean two-dimensional materials, such as a thin layer of graphene, behave in much the same way.

A sheet of paper released from a window flutters, tumbles, and sometimes pauses flat for a second. Until now, to honestly predict such behavior, you had to run millions of equations on supercomputers for every drop of air. That's like simulating every atom of a cash register to count change at a store. The new approach is smarter.

A drop of a thick cornstarch-water mixture falls onto a table. Normally, such a mixture solidifies instantly upon a sharp impact: you can even run across a pool filled with it. But in this experiment, things went differently. The high-speed camera captured that in the first instant after contact, the drop spreads out like an ordinary liquid.

When a planet approaches its star to a critical distance, tidal forces, the result of a sharp gradient in gravity between the near and far sides of the celestial body, tear it apart. This process ignites a cosmic funeral pyre: the planet's debris forms a glowing accretion disk around the star.

Water swirls into a ring, and that ring flies through the bulk without breaking apart. Such vortex rings, from smoke rings to underwater currents, follow laws that are hard to capture on paper. Usually, the flow is divided into millions of cubic cells, and each one is tracked.

A fusion reactor resembles a giant boiler where hydrogen is 'cooked' into helium. The plasma inside is heated to 150 million degrees — ten times hotter than the Sun's core. But like any boiler, scale forms: harmful impurities that settle on the walls and quench the plasma.