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muNavierStokes

muNavierStokes is a direct numerical simulation (DNS) of the incompressible Navier–Stokes equations using a pseudo-spectral method on a triply-periodic box. Fast Fourier transforms, field storage and the (optionally MPI-parallel) domain decomposition are provided by µGrid, which also supplies the GPU backend.

Highlights

  • Pseudo-spectral solver. The velocity field is advanced in its Fourier representation; the nonlinear term is formed in real space and the pressure is eliminated by a divergence-free (Leray) projection.
  • Rotational form + RK4. The advection term uses the rotational form \(u\times\omega\), integrated in time with a classical fourth-order Runge–Kutta step that allocates nothing per stage.
  • 2/3-rule dealiasing. Aliasing error from the nonlinear product is removed by band-limiting to the lower two thirds of the spectrum.
  • MPI-parallel and GPU-ready. The same code runs serially, across MPI ranks (pencil-decomposed FFTs), or on the GPU — selected at run time.
  • One executable. simulate.py runs a Taylor–Green vortex or forced isotropic turbulence and streams the velocity field to NetCDF.

A first run

# Taylor-Green vortex on a 64^3 grid (serial)
python simulate.py --initial-condition taylor-green -n 64 64 64

# forced isotropic turbulence on 4 MPI ranks
mpirun -np 4 python simulate.py --initial-condition turbulence

# on the GPU
python simulate.py --device cuda -i taylor-green

Where to go next

  • Installation — dependencies and how to build the MPI/GPU-enabled µGrid this solver needs.
  • Usage — the simulate.py driver, its options, and the post-processing scripts.
  • Physics — governing equations, the Fourier representation, and dealiasing.
  • Implementation — the NavierStokes solver, the RK4 stepper, and the µGrid field interface.
  • GPU — how the solver runs device-agnostically on CPU or GPU.
  • Benchmark — single-CPU, multi-CPU (MPI) and single-GPU timing on a real machine.

History

muNavierStokes is part of the µSpectre project, an open-source platform for FFT-based continuum mesoscale modelling. It is built on the standalone µGrid grid library.

License

muNavierStokes is free software, distributed under the terms of the GNU Lesser General Public License (see LICENSE).