# 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…

## 2 Citations

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A spectral method to solve the heat equation in a closed cylinder, achieving a near-optimal O(N logN) complexity and high-order, spectral accuracy and a framework by which this heat equation solver could be applied to the incompressible Navier–Stokes equations.

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