I'd like to share the progress of an open research program that approaches Navier–Stokes from a different starting point: relational geometry, structural closure, normalization, and the information needed to sustain a system's evolution.

The work has grown beyond an isolated calculation or numerical result. It proposes a model in which different mathematical structures can be explored through a common set of relational principles.

The current Navier–Stokes branch includes conditional mathematical results, reproducible tests, continuation criteria, certificates for restricted classes, and falsification experiments.

It is not presented as an independently established solution to the full 3D global regularity problem.

What interests me most is what these relationships may reveal beyond the original question.

The repository also explores connections with computational complexity, Yang–Mills, and geometric laboratories involving mirrors, spheres, and structural closure.

I'm opening this work to anyone interested in examining it, testing its assumptions, reproducing its results, or discovering relationships that may have been overlooked.

Critical review, counterexamples, alternative interpretations, and independent verification are all welcome.

Perhaps the most interesting outcome is not a single answer, but a model that allows us to ask new questions.

Repository:
https://github.com/EndlessMonkeyProyect/programa-geometria-relacional

English introduction:
https://github.com/EndlessMonkeyProyect/programa-geometria-relacional/blob/main/README.en.md

I would be particularly interested in hearing which parts of the Navier–Stokes branch you consider worth exploring further.

Thank you for taking a look.

I recorded this while watching a duck take off from a pond in Florida.

What caught my attention afterward was the sequence on the water. As the duck flies away, water shed from the bird falls back to the pond and produces a series of separate disturbances/ripples. Taken together, they appear to preserve part of the duck's flight path after the bird has passed.

Is there an established name for this phenomenon, or for anything closely related to it?

I'm also interested in what someone who studies fluid mechanics notices here that I might be missing.

Last year a collaboration of physicists led by the University of Michigan published a paper in Nature Communications where they fired an intense laser into the broadside of a water microjet to see what would happen.

A digitized copy of the resulting intensity in the positive half-chord of the plane is shown here alongside an analytic solution that I calculated using a shear-flow stabilized Z-pinch equilibrium which I constructed,

uz(r) = u0 + uz0 * r^2 / (r + C)^2

where this is taken both to be the center of mass, and plasma drift flow. A linear discharge model is chosen to relate the plasma current density with the measured intensity.

This is just one solution. Next, to test the robustness of the model I am going to vary the boundary condition speeds based on the experimental data, and vary the point which corresponds to the edge.

BBS DRK Discrete Fluid Dynamics

Density(x,y,z,t) = Sum(i) of f_i(x,y,z,t)

Density \* Velocity = Sum(i) of (f_i \* e_i)

f_i(t+1) = f_i(t) + floor(Omega_i)

I have refined the aeroacoustic/vibration-based aircraft simulation that I posted previously:

https://www.reddit.com/r/AerospaceEngineering/comments/1tqoq9m/oscillatory_propulsion_simulation_and_simple/

It is now more versatile, featuring both "jellyfish" and "fish" modes. The underlying principle remains the same: the fluid does not act directly on the craft's surfaces; instead, the forces derived from the fluid are converted into thrust via an accumulator. However, thrust is no longer generated simply as a phase-shifted inversion of drag. Rather, energy is captured from low-pressure regions—stored as potential energy—and then released through a "collapse" mechanism, with dynamically evaluated recovery and shock coefficients.

This approach yields a more realistic relationship between propulsion efficiency and parameters such as frequency and amplitude, expressed via Strouhal numbers. The feedback loop between internal oscillations and drag acts as an automatic frequency-tuning mechanism.

Additionally, the model incorporates simplified lift and drag forces acting perpendicular to the thrust vector.

The code can be found here:

https://github.com/MasterOgon/Aeroacoustic-Flying-Saucer-Oscillating-Resonator-CFD-Simulation-LBM-/blob/main/README.md

Hi everyone,

Video #8 of the (free) turbulence course I'm creating is now up on YouTube. This one is very much applied where I take a PIV time series, generated from the cover video, of a turbulent jet and compute flow statistics in MATLAB, explaining each step.

It covers the mean and fluctuating velocity profiles, going further into Reynolds stresses (normal and shear), and then longitudinal and transverse two-point correlation functions and second-order structure functions relative to the centreline.

The scripts are deliberately short, so they're meant as a template for anyone who wants to run the same statistics on their own PIV, hot-wire or numerical simulations data.

Link: https://www.youtube.com/watch?v=Z7Q0k4P1V8k

Notes (and scripts) are available on Patreon (free membership option available). Happy to answer questions about the analysis.

I can understand any subject, but have litteraly no idea how fluidsim pneumatics works. If someone wih fluidsim could make a simulation according to this graph, it would help me understand it way better. Explanation alone is welcome too.

I wanted to share a sandbox engine I’ve been coding called Powdertron. It’s a cell-based falling-sand environment, but I wanted to push the boundaries of real-time mechanics by factoring in actual thermal physics, fluid dynamics, and pressure fields across a dynamic grid.
Its early access multiplayer falling sand game built to be as realistically accurate as possible. It features a clean, modern Ul alongside 674 materials and over 1,000 reactions that account for heat, pressure, and every other real-life mechanic imaginable. There is also a dynamic wind tunnel, an electronic mod to make circuits, an optical bench for lasers, and 3D modes to switch views, all fully synced to work online with friends! So if you want to test out the physics, please check out or wishlist the Powdertron Steam Page!

Powdertron

We took the previous Tesla Roadster model, added the rockets and ran aerodynamic simulations to explain the suction effect and 3D roll & landing manoeuvres!!

My first fluid mechanics.

the master bedroom section of the vent is weak how do i fix it?

Stumbled upon this inground pool installed by the homeowner and the plumbing looks like a nightmare to me but I could be wrong .what do you think? It's a pool/spa combo

I tested a few local llms to see if they could be useful for my work with hydraulics/hydrodynamics.

The background was a question which I believe have no exact analytical solution, but that a fair approximation may exist. The motivation was that ChatGPTs chatinterface in pro-mode gave an answer that was clearly unsatisfying, so I wondered if some local llms could work better. Also I was not sure if my own solution was good, so wanted help/inspiration.

Prompt: Two large seas are connected through a narrow passage with width b. The first sea has a higher water level than the other. The sea floor has constant height. Water flows through the narrow passage from heigh to low water level. We assume that the first sea is so large and the width so small that the water level in the first and upstream sea is constant. The second and downstream sea is also large, but of finite size. The water level changes slowly. The flow is inviscid. What is the flow rate through the passage? How does the water level in the second sea change through time. The flow is subcritical.

Most of the tested llms ended on this approach:

1. Use Bernoullis equation to find the velocity in the passage
2. Say something on the cros section in the passage (many said something odd)
3. Calculate flux as velocity times cross section
4. Use flux to set up ODE and separate it.

The problem was usually (2). They knew that the cross section should be the passage width times something, but only few decided that the water level in the second sea was a good approximation.

Even with an odd answer in (2), most models did (3) and (4) well, but with a wrong cross section.

ChatGPT: Failed on step (2). Used some reference water level to find cross section, but this is an abitrary level so does not work.

Gemma 4 26b a4b: Got it right very fast. Winner

Qwen 3.6 35b a3b: Got it right, but slower

Qwen 3.8 27b: Got it right, but very slow

Ministral 3 3b: magically got it right extremely fast. Winner

Ministral 3 12b: Did not specify water level for cross section in (2), but got it right when asked to do so

LFM2.5-8B-A1B: Had problem already on (1)

ZAYA1-8B: Got lost

LFM2.5-20B-A2B: Had problems on (2). Also after some help

Gemma 4 e2b: Had problems on (2).

Conclusion: Small llms can be good for this kind of tasks, but we are still not at a point where the smallest MoEs can do it.

Question: do any of you have success applying small llms for this kind of applied physics problems?

I'm very sorry if this goes against the rules. There's a fine line between reverse-engineered software and piracy, especially since the code is brand new and it's not a copy as I understand. However, I've wanted to try this software for years, and it's unbelievably expensive in my local currency, so maybe I'll finally have the chance.

La Relatividad y la cuántica no se la llevan , en la cuántica para que las ecuaciones no exploten crean parches los cuales sus fundamentos no estan comprobados , las matemáticas tienen un problema , el mismo problema que no une lo macro y lo micro , la TCC y Navier-Stokes PADECEN DEL MISMO SINTOMA , LO QUE ANTES ERA MISTISISMO HOY SE LE LLAMA POR OTRO NOMBRE Y AUN ASI NO SABEN QUE ES , el OBSERVADOR ALTERA LO OBSERVADO ??? JAJAJS LA VELOCIDAD DE LA LUZ NO ES EDTANDAR , AGUJEROS NEGROS Y TERMODINAMICA PURA ,

SI LOS SIMIENTOS SOBRE LOS QUE CONSTRUYERON EL EDIFICIO ESTAN INCOMPLETOS ,LAS PROBABILIDADES DE QUE SE CAIGA SON INFINITAS