🌪️ Turbulox

Turbulence in a box.

taylorgreen.mp4

🚀 Installation

This package is in active development, and breaking changes are expected. Install the latest version with

using Pkg
Pkg.add("https://github.com/agdestein/Turbulox.jl")

👮 The rules

You solve the incompressible Navier-Stokes equations with the following rules:

• The domain is always a cube $\Omega = [0,1]^d$ with $d \in { 2, 3}$. Side length: $L = 1$.
• Annoying boundary conditions are forbidden (periodic box only).
• The flow is incompressible.
• The grid is uniform and staggered.
• There is no pressure 🥵.
• Single process, single GPU. Nowadays you can fit $1000^3$++ grid points on a single H100.

You get to choose:

• The resolution $n^d$
• The viscosity $\nu$ (but don't make it too large!)
• The dimension $d$
• The discretization order of accuracy $o \in {2, 4, 6, \dots}$
• Body force $f$

⚔️ The battle

🧙 Plug in your turbulence closure 🪄. Compete.

Todo:

• Leaderboard

📚 Down to business

The equations:

$$\partial_j u_j = 0$$

$$\partial_t u_i + \partial_j (u_i u_j) = -\partial_i p + \nu \partial_{jj} u_i + f_i$$

Discretization: Fully conservative combination of central difference stencils from Morinishi et al.

🫣 Outlook

Disretization orders:

• Second order
• Fourth order
• Sixth order
• Eighth order
• Tenth order

Goodies:

• The velocity gradient and its waste products
  • Invariants
  • Turbulence statistics and scale numbers
• Spectra
  • Energy
  • Reference slope $C_K \epsilon^{2/3} k^{-5/3}$

Closure models:

• All the classics
  • Smagorinsky
  • Gradient model (Clark)
  • Vreman
  • Verstappen
  • $\sigma$-model
• Nice interface for plugging in new ones

Differentiability

• Enzyme-compatibility

Data-generation

• Add batch dimension and loop over it in kernels (maybe)
• Data-consistency: Export commutator errors and sub-filter tensors consistent with how they appear in the discrete equations