4 ms·

Jaw-dropping? Maybe. Realistic? Nope. I work in a group with scientists whose sole job is to solve the Navier-Stokes equations. Now that's realistic.

pvnick 14y ago
You must just be a hoot at parties
- coherentpony 14y ago
  Oh, you haven't the slightest. :)
aolol 14y ago
Perhaps you could elaborate on this. I do agree that the title and video give slightly more credit than is due based on the current state of fluid dynamics knowledge. However do you mean your group is searching for closed-form solutions to NS or are you generating approximate numerical solutions (CFD)?
- coherentpony 14y ago
  Approximate solutions are found computationally. Non-trivial closed-form solutions are hopeless. Existence of solutions is a little less hopeless. Existence of solutions over small time horizons has been proven. This is all in three space dimensions. There is a theorem stating that if global-time solutions exist and are unique, then computationally computed approximate solutions are 'good'. Moreover, they get better as you refine the computational domain.
  - noname123 14y ago
    Is finite element method good enough? Can you provide a concrete example where approximation is not good enough.
    - coherentpony 14y ago
      Special approximations called 'Galerkin approximations' converge. Finite element methods are a special case of Galerkin methods. Finite element methods are good enough.
- starpilot 14y ago
  At this time NS solutions are all approximate, but there's a huge gulf between plausible-looking fluids (as in story), and fluids with pressure, velocity distributions accurate enough for analysis (to design an airplane). And within the latter there are further demarcations depending on the type of fluid analysis, where errors manifest as extremely subtle (pressure looks slightly high, vortices dissipate too quickly or too slowly) and judging the best algorithm for a problem becomes almost an art.
mercnet 14y ago
I am SQA Engineer for Autodesk Simulation CFD and our recent 2014 version has free surface modeling: https://www.youtube.com/watch?v=WNKHf937Qt0 https://www.youtube.com/watch?v=WNKHf937Qt0. It does make pretty pictures but as you mentioned solving navier-stokes equations can get complicated :)
- coherentpony 14y ago
  Beautiful. Those boundary conditions must suck!

pvnick 14y ago

You must just be a hoot at parties

coherentpony 14y ago
Oh, you haven't the slightest. :)

aolol 14y ago

Perhaps you could elaborate on this. I do agree that the title and video give slightly more credit than is due based on the current state of fluid dynamics knowledge. However do you mean your group is searching for closed-form solutions to NS or are you generating approximate numerical solutions (CFD)?

coherentpony 14y ago
Approximate solutions are found computationally. Non-trivial closed-form solutions are hopeless. Existence of solutions is a little less hopeless. Existence of solutions over small time horizons has been proven. This is all in three space dimensions. There is a theorem stating that if global-time solutions exist and are unique, then computationally computed approximate solutions are 'good'. Moreover, they get better as you refine the computational domain.
- noname123 14y ago
  Is finite element method good enough? Can you provide a concrete example where approximation is not good enough.
  - coherentpony 14y ago
    Special approximations called 'Galerkin approximations' converge. Finite element methods are a special case of Galerkin methods. Finite element methods are good enough.
starpilot 14y ago
At this time NS solutions are all approximate, but there's a huge gulf between plausible-looking fluids (as in story), and fluids with pressure, velocity distributions accurate enough for analysis (to design an airplane). And within the latter there are further demarcations depending on the type of fluid analysis, where errors manifest as extremely subtle (pressure looks slightly high, vortices dissipate too quickly or too slowly) and judging the best algorithm for a problem becomes almost an art.

mercnet 14y ago

I am SQA Engineer for Autodesk Simulation CFD and our recent 2014 version has free surface modeling: https://www.youtube.com/watch?v=WNKHf937Qt0 https://www.youtube.com/watch?v=WNKHf937Qt0. It does make pretty pictures but as you mentioned solving navier-stokes equations can get complicated :)

coherentpony 14y ago
Beautiful. Those boundary conditions must suck!