Nature

Finite Element Methods for Navier-Stokes Equations

Finite element methods (FEM) have emerged as a pivotal class of numerical techniques for solving the Navier–Stokes equations, the mathematical foundation for modelling fluid flow. These methods ...
Wired

Mathematicians Second-Guess Centuries-Old Fluid Equations

The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...
Quanta Magazine

Using AI, Mathematicians Find Hidden Glitches in Fluid Equations

Nearly 200 years ago, the physicists Claude-Louis Navier and George Gabriel Stokes put the finishing touches on a set of equations that describe how fluids swirl. And for nearly 200 years, the ...
New Scientist

These centuries-old equations predict flowing fluid – until they don’t

The following is an extract from our Lost in Space-Time newsletter. Each month, we hand over the keyboard to a physicist or mathematician to tell you about fascinating ideas from their corner of the ...
Quanta Magazine

Deep Learning Poised to ‘Blow Up’ Famed Fluid Equations

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...
Nature

Finite Element Methods for Incompressible Flow and Navier-Stokes Equations

Finite Element Methods (FEM) have emerged as a pivotal computational tool in the simulation of incompressible flows and the Navier-Stokes equations. By discretising the domain, these techniques offer ...