• Corpus ID: 232428150

An optimal complexity spectral method for Navier-Stokes simulations in the ball

@article{Boulle2021AnOC,
  title={An optimal complexity spectral method for Navier-Stokes simulations in the ball},
  author={Nicolas Boull'e and Jonasz Słomka and Alex Townsend},
  journal={ArXiv},
  year={2021},
  volume={abs/2103.16638}
}
Summary We develop a spectral method for solving the incompressible generalized Navier– Stokes equations in the ball with no-flux and prescribed slip boundary conditions. The algorithm achieves an optimal complexity per time step of  ( 𝑁 log 2 ( 𝑁 )) , where 𝑁 is the number of spatial degrees of freedom. The method relies on the poloidal-toroidal decomposition of solenoidal vector fields, the double Fourier sphere method, the Fourier and ultraspherical spectral method, and the spherical… 

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