The shallow-water equations (SWE) are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. The shallow-water equations in unidirectional form are also called (de) Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant.
Shallow Water Equations - RDycore: A River / Flooding dynamical core for E3SM
The two-dimensional shallow water equations can be written in the conservative form
lisyarus/webgpu-shallow-water
GPU shallow water solver using the virtual pipes model using WebGPU
Navier-Stokes Equation - Clay Mathematics Institute
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Navier-Stokes lost in translation: Why Lean verification of AI...
Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this...
Rainbow Peak Part 7 | Modeling Waterfalls
tristanbuckmaster (@tristanbuckmaster@mastodon.social)
Today, Levent Alpöge and I have made public three results: finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler. https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/euler.pdf https://cims.nyu.edu/~tristanb/ipm.pdf https://cims.nyu.edu/~tristanb/boussinesq.pdf https://github.com/tristanbuckmaster/fluid_lean
Computational OT #4 - Gradient flow and diffusion models
A course on computational Optimal Transport
Sécheresse : « Notre principal défi est d’abord de renoncer à l’illusion de l’abondance de l’eau »
Face au changement de régime hydroclimatique, nos systèmes de répartition de l’eau ne sont plus adaptés, affirme, dans un entretien au « Monde », la géographe Sara Fernandez. Selon elle, il est urgent d’interroger collectivement l’utilité des usages et leur capacité à aggraver ou à atténuer les effets des phénomènes extrêmes.
GitHub - wagoodman/dive: A tool for exploring each layer in a docker image
A tool for exploring each layer in a docker image. Contribute to wagoodman/dive development by creating an account on GitHub.
Adding Realistic Rivers to Random Terrain
Discusses a method for adding rivers to randomly generated terrain that adds a realistic touch.
Docs | Graze Turbostream
Details about the turbostream, a hydrated-reference variation of the jetstream
AI Has Solved One of Math’s $1 Million Millennium Prize Problems | Quanta Magazine
Mathematicians at OpenAI showed that the Navier-Stokes equations, which describe how fluids flow, can sometimes “blow up.” But the massive result is not without controversy.
bend/paper/BendTT.pdf at main · bendlang/bend
Bend 2: a fast language that blocks AI mistakes via proof. Install: curl -fsSL https://bend-lang.com/install.sh | sh - bendlang/bend
If you aren’t used to staring at math, Poisson’s equation looks a little intimidating: