#navierstokes — Public Fediverse posts

Navier-Stokes fluid simulation explained with Godot game engine

https://myzopotamia.dev/navier-stokes-fluid-simulation-explained-with-godot

#HackerNews #NavierStokes #GodotGameEngine #FluidSimulation #GameDevelopment #TechExploration

Navier-Stokes fluid simulation explained with Godot game engine

https://myzopotamia.dev/navier-stokes-fluid-simulation-explained-with-godot

#HackerNews #NavierStokes #GodotGameEngine #FluidSimulation #GameDevelopment #TechExploration

📢 MOSS Season 2 continues next week Thursday!

🎙️ Speaker: Claudia García (Universidad de Granada, Spain)

🗣️ Talk title: Patterns and equilibria in incompressible fluids

🗓️ Thursday, 9 April 2026 • 🕓 16:00 CEST • Online

A talk on 2D Euler/Navier–Stokes, relative equilibria, and coherent vortex patterns through bifurcation theory.

👉 Scan the QR code in the image to join the mailing list and receive the online access link.

#Mathematics #FluidDynamics #NavierStokes #EulerEquations #PDE

📢 MOSS Season 2 continues next week Thursday!

🎙️ Speaker: Claudia García (Universidad de Granada, Spain)

🗣️ Talk title: Patterns and equilibria in incompressible fluids

🗓️ Thursday, 9 April 2026 • 🕓 16:00 CEST • Online

A talk on 2D Euler/Navier–Stokes, relative equilibria, and coherent vortex patterns through bifurcation theory.

👉 Scan the QR code in the image to join the mailing list and receive the online access link.

#Mathematics #FluidDynamics #NavierStokes #EulerEquations #PDE

Basics of Numerical Weather Prediction (NWP):

1. THE HORIZONTAL MOMENTUM EQUATION:
\[
\frac{d\mathbf{V}}{dt} + f\hat{k} \times \mathbf{V} = -\nabla \phi + \frac{\sigma}{p_s} \frac{\partial \phi}{\partial \sigma} \nabla p_s + \mathbf{F}
\]

2. THE CONTINUITY EQUATION:
\[
\frac{\partial p_s}{\partial t} + \nabla \cdot (p_s \mathbf{V}) + \frac{\partial}{\partial \sigma}(p_s \dot{\sigma}) = 0
\]

3. THE THERMODYNAMIC ENERGY EQUATION:
\[
\frac{1}{R} \frac{d}{dt} \left[ \sigma \frac{\partial \phi}{\partial \sigma} \right] + \frac{RT}{C_p p} \left[ p_s \dot{\sigma} + \sigma\dot{p_s} \right] = -Q
\]

4. HYDROSTATIC EQUATION:
\[
\frac{\partial \phi}{\partial \sigma} = -\frac{RT_v}{\sigma}
\]

5. SURFACE PRESSURE TENDENCY EQUATION:
\[\displaystyle
\frac{\partial p_s}{\partial t} = -\int_{0}^{1} \nabla\cdot (p_s \mathbf{V}) \, d\sigma
\]

6. MOISTURE EQUATION:
\[\displaystyle
\frac{\partial}{\partial t} (p_s q) + \nabla\cdot (p_s q \mathbf{V}) + \frac{\partial}{\partial \sigma} (p_s q \dot{\sigma}) = p_s S
\]

The six primary unknowns are: \(\mathbf{V}\) (horizontal wind velocity), \(p_s\) (surface pressure), \(T\) (temperature), \(q\) (specific humidity or moisture), \(\phi\) (geopotential), and \(\dot{\sigma}\) (sigma velocity or vertical velocity in \(\sigma\)-coordinates).

#NWP #Weather #NumericalWeatherPrediction #Meteorology #Climate #ClimateScience #Earth #EarthScience #ClimateChange #ClimateSciences #Science #WeatherPrediction #Humidity #Moisture #Pressure #Velocity #SurfacePressure #HydrostaticEquation #WeatherPrediction #Ocean #Atmosphere #AOS #ClimateDynamics #WeatherDynamics #Geopotential #SigmaVelocity #VerticalVelocity #MoistureEquation #Thermodynamics #Dynamics #NavierStokes

Imagine being a brilliant physicist/mathematician and still avoiding the most important problems because your career depends on publishing frequent papers, not solving the biggest mysteries in the world.

That's why you can't do things like this in academia.

https://english.elpais.com/science-tech/2025-06-24/spanish-mathematician-javier-gomez-serrano-and-google-deepmind-team-up-to-solve-the-navier-stokes-million-dollar-problem.html

#NavierStokes #GoogleDeepMind #DeepMind #MillenniumProblems #Existence #Smoothness #Fluid #FluidDynamics #Turbulence #Dynamics #TurbulentFlows #Research #Engineering #Physics #Math #Maths #Mathematics #UnsolvedProblems #BiggestMystery #Flows #MillionDollarProblem

🌊 Scientists have advanced in understanding turbulence, a long-standing puzzle for physicists. This progress aids in solving the Navier–Stokes equations, a major challenge in math and physics, and a Millennium Prize Problem by the Clay Mathematics Institute. Recent developments are crucial for fluid dynamics, impacting engineering, meteorology, and more.

@goodnews

#GoodNews #Physics #Turbulence #NavierStokes #ScienceBreakthrough
https://edition.cnn.com/2025/02/06/science/turbulence-physics-oldest-unsolved-problem/index.html

🌊 Scientists have advanced in understanding turbulence, a long-standing puzzle for physicists. This progress aids in solving the Navier–Stokes equations, a major challenge in math and physics, and a Millennium Prize Problem by the Clay Mathematics Institute. Recent developments are crucial for fluid dynamics, impacting engineering, meteorology, and more.

@goodnews

#GoodNews #Physics #Turbulence #NavierStokes #ScienceBreakthrough
https://edition.cnn.com/2025/02/06/science/turbulence-physics-oldest-unsolved-problem/index.html

Researchers claim to have solved Hilbert’s sixth problem by unifying three theories of #FluidDynamics at different levels of granularity:

+ Newton’s laws of motion at the microscopic level where fluids are composed of particles - little billiard balls bopping around and occasionally colliding

+ The Boltzmann equation at the mesoscopic level where the equation considers the likely behavior of a typical particle

+ Euler and #NavierStokes equations at the macroscopic level where the fluids are a single continuous substance

https://www.scientificamerican.com/article/lofty-math-problem-called-hilberts-sixth-closer-to-being-solved

Preprint https://arxiv.org/abs/2503.01800

Researchers claim to have solved Hilbert’s sixth problem by unifying three theories of #FluidDynamics at different levels of granularity:

+ Newton’s laws of motion at the microscopic level where fluids are composed of particles - little billiard balls bopping around and occasionally colliding

+ The Boltzmann equation at the mesoscopic level where the equation considers the likely behavior of a typical particle

+ Euler and #NavierStokes equations at the macroscopic level where the fluids are a single continuous substance

https://www.scientificamerican.com/article/lofty-math-problem-called-hilberts-sixth-closer-to-being-solved

Preprint https://arxiv.org/abs/2503.01800

An Article in the Annual Review of Condensed Matter Physics on Turbulence by KR Sreenivasan and J Schumacher
https://www.annualreviews.org/content/journals/10.1146/annurev-conmatphys-031620-095842

What is the turbulence problem, and when can we say it’s solved? 🌪️ This deep dive by Sreenivasan & Schumacher explores the math, physics, and engineering challenges of turbulence—from Navier-Stokes equations to intermittency and beyond. A must-read for anyone fascinated by chaos, complexity, and the unsolved mysteries of fluid dynamics! 🌀

A summary of the talk presented by KR Sreenivasan in December 2023 at the International Center for Theoretical Sciences (ICTS-TIFR) in Bengaluru, as part of a program on field theory and turbulence.
https://www.youtube.com/watch?v=fwVSBYh-KC4

"Field Theory and Turbulence" program link: https://www.icts.res.in/discussion-meeting/ftt

#FluidDynamics #Physics #NavierStokes #UnsolvedMystery #Mechanics #Dynamics #FluidMechanics #Science #Chaos #TurbulentMotion #Randomness #Chaotic #Fluid #ClassicalMechanics
#Turbulence

Only a genderfluid creature can hope to solve the Navier-Stokes Equations existence and uniqueness problem.

#NavierStokes #genderfluid

Only a genderfluid creature can hope to solve the Navier-Stokes Equations existence and uniqueness problem.

#NavierStokes #genderfluid

So, I mentioned already that we cannot really model #lava flows. The main reasons for that is that we don't actually know how lava behaves, at least not in sufficient detail.

Of course, lava is a fluid, and a (very) viscous one at that, so we know that it follows the Navier–Stokes equations. We also know that its behavior is heavily dependent on temperature, so we know that we also need the heat equation, with both kinds of boundary conditions (conduction to ground, and radiation on the free surface).

And that's all we know. Seriously.

OK, not really, but everything else is extremely uncertain. When modeling a viscous fluid (like lava, or any other geophysical flow for the matter), the first thing you need to know is what the viscosity is. And for lava, we don't know. There's a lot of things we do know, but not enough.
For example, we know that the viscosity depends on temperature, chemical composition, degree of crystalization, amount and types of volatiles in the melt, and so on and so forth. But we don't exactly know the laws relating the viscosity to all of these chemical and physical properties.

2/

#NavierStokes #NavierStokesEquations

So, I mentioned already that we cannot really model #lava flows. The main reasons for that is that we don't actually know how lava behaves, at least not in sufficient detail.

Of course, lava is a fluid, and a (very) viscous one at that, so we know that it follows the Navier–Stokes equations. We also know that its behavior is heavily dependent on temperature, so we know that we also need the heat equation, with both kinds of boundary conditions (conduction to ground, and radiation on the free surface).

And that's all we know. Seriously.

OK, not really, but everything else is extremely uncertain. When modeling a viscous fluid (like lava, or any other geophysical flow for the matter), the first thing you need to know is what the viscosity is. And for lava, we don't know. There's a lot of things we do know, but not enough.
For example, we know that the viscosity depends on temperature, chemical composition, degree of crystalization, amount and types of volatiles in the melt, and so on and so forth. But we don't exactly know the laws relating the viscosity to all of these chemical and physical properties.

2/

#NavierStokes #NavierStokesEquations

So there's apparently a #metal song mentioning the #NavierStokes equations now.

https://youtu.be/Jy99ywCp3qU

#music #CFD #meteorology #parody

So there's apparently a #metal song mentioning the #NavierStokes equations now.

https://youtu.be/Jy99ywCp3qU

#music #CFD #meteorology #parody

These fluid sim bugs ain't gonna fix themselves. #watercolor #simulation #BigWetPixels #procedural #DebugView #algorithmic #NavierStokes

I'm midway through a (major, long overdue) overhaul of the fluid transport layer of my watercolor simulation. Made some good progress over the weekend. But more importantly: I made lots of new bugs. Glorious, unrepentant, face-eating bugs. I almost don't have the heart to squash them.

https://vimeo.com/cassidy/big-wet-pixels-10

#BigWetPixels #watercolor #simulation #DebugView #generative #algorithmic #procedural #NavierStokes

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

#ThisMonthInFluiddyn it is. Let's go 😎

🔹@PierreAugier and friends are finishing up an article, so as a side project they released #formattex and #formatbibtex based on #TexSoup and #BibtexParser

https://pypi.org/project/formattex/
https://pypi.org/project/formatbibtex/

> a simple and uncompromising #Latex code formatter

🔹Version 0.7.4 of #fluidsim and fluidsim-core were released containing a refactored energy spectra for #NavierStokes solvers and other bug fixes

https://pypi.org/project/fluidsim/

#fluiddyn

Predicting weather is a complex dance of physics and math. The Navier-Stokes equations help us model fluid motion, which is essential for forecasting storms and understanding climate patterns. #WeatherForecasting #NavierStokes

Predicting weather is a complex dance of physics and math. The Navier-Stokes equations help us model fluid motion, which is essential for forecasting storms and understanding climate patterns. #WeatherForecasting #NavierStokes

12 steps to #NavierStokes equations? Google Bard can help you work through this classic tutorial by yours truly. Nice! But don't forget to try things on your own and figure out what each line of code is doing. Start small, and build!
#CFD https://g.co/bard/share/5fd863fa5de6

12 steps to #NavierStokes equations? Google Bard can help you work through this classic tutorial by yours truly. Nice! But don't forget to try things on your own and figure out what each line of code is doing. Start small, and build!
#CFD https://g.co/bard/share/5fd863fa5de6

Learned a lot from my lunch with Thomas Hou today, who recently finally vindicated his 10 year quest of showing the (axisymmetric, incompressible) Euler equation blows up. https://arxiv.org/abs/2210.07191
#PDE #NavierStokes #Euler #Math #Physics #MachineLearning #DeepLearning

Learned a lot from my lunch with Thomas Hou today, who recently finally vindicated his 10 year quest of showing the (axisymmetric, incompressible) Euler equation blows up. https://arxiv.org/abs/2210.07191
#PDE #NavierStokes #Euler #Math #Physics #MachineLearning #DeepLearning

Navier–Stokes momentum equations:
\[\overbrace{\overbrace{\underbrace{\dfrac{\partial\mathbf{u}}{\partial t}}}^\text{Variation}_\text{Local}+\overbrace{\underbrace{(\mathbf{u}\cdot\nabla)\mathbf{u}}_\text{Convective}}^\text{Divergence}}^\text{Inertia/Acceleration}=\overbrace{\underbrace{-\dfrac{1}{\rho}\nabla p}_\text{Internal}+\underbrace{\mathbf{g}}_\text{External}}^\text{Source terms}+\overbrace{\underbrace{\nu\nabla^2\mathbf{u}}_\text{Viscous}}^\text{Diffusion}\]
#NavierStokes #FluidDynamics

> One of the central problems in fluid dynamics is to figure out if the [Euler] equations ever fail, outputting nonsensical values that render them unable to predict a fluid’s future states.
> Mathematicians have long suspected that there exist initial conditions that cause the equations to break down. But they haven’t been able to prove it.
> In a preprint posted online last month, a pair of mathematicians has shown that a particular version of the Euler equations does indeed sometimes fail.
...
> Perhaps in some situations, the equations will proceed as expected, producing precise values for the state of the fluid at any given moment, only for one of those values to suddenly skyrocket to infinity. At that point, the Euler equations are said to give rise to a “singularity” — or, more dramatically, to “blow up.”
> Once they hit that singularity, the equations will no longer be able to compute the fluid’s flow.
...

Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations
https://www.quantamagazine.org/computer-helps-prove-long-sought-fluid-equation-singularity-20221116/

Very important and interesting work, if you're a mathematician, a physicist or an engineer that has ever 'crashed' with Euler/Navier-Stokes equations.

#math #physics #fluids #euler #navierstokes #equations #singularities

Hoe staat het met de Navier-Stokesvergelijkingen? Ze zijn 200 jaar oud, bruikbaar in de praktijk dankzij computerberekeningen, maar veel van de achterliggende #wiskunde is nog altijd onbegrepen. Over de huidige stand van zaken schreef ik voor #NRC.
#NavierStokes
#millenniumproblem
#milliondollar
https://www.nrc.nl/nieuws/2022/12/09/alles-stroomt-maar-de-wiskunde-daarachter-is-nog-goeddeels-onbegrepen-a4150762

Hoe staat het met de Navier-Stokesvergelijkingen? Ze zijn 200 jaar oud, bruikbaar in de praktijk dankzij computerberekeningen, maar veel van de achterliggende #wiskunde is nog altijd onbegrepen. Over de huidige stand van zaken schreef ik voor #NRC.
#NavierStokes
#millenniumproblem
#milliondollar
https://www.nrc.nl/nieuws/2022/12/09/alles-stroomt-maar-de-wiskunde-daarachter-is-nog-goeddeels-onbegrepen-a4150762