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The secret: T³ periodic domain + Fourier orthogonality = the weak solution is just a curve in coefficient space. Not a field. A curve.
Temporal lifting samples that curve densely where it bends hardest. Standard DNS crashes from CFL blowup. This doesn't - because we're not fighting the geometry, we're riding it.
Results:
Taylor-Green Re=10⁵: BKM=37.1, stable through full vortex-stretching cascade Kolmogorov Re=10⁸: 0.07% dissipation error 128³ grid → 411³ effective resolution (spectral super-resolution from temporal oversampling) Hardware: 8GB laptop, no GPU
No artificial dissipation. No hyperviscosity. Unmodified Navier-Stokes unlike all other DNS. GitHub link to code and data in the paper (linked)
Taylor-Green Re=10⁵: BKM=37.1, stable through full vortex-stretching cascade Kolmogorov Re=10⁸: 0.07% dissipation error 128³ grid → 411³ effective resolution (spectral super-resolution from temporal oversampling) Hardware: 8GB laptop, no GPU
No artificial dissipation. No hyperviscosity. Unmodified Navier-Stokes unlike all other DNS. GitHub link to code and data in the paper (linked)
What's the significance of those particular Reynold's numbers? 10^8 seems high for incompressible flow, but maybe I misread something.
> because we're not fighting the geometry, we're riding it
Don’t let ChatGPT write summaries for you (please edit the comment to be real)
Don’t let ChatGPT write summaries for you (please edit the comment to be real)
I like the idea behind this. Thanks to the author.
Is there any reason to believe this isn’t an AI-assisted crank publication?