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arXiv · 1607.00566

Fourier solution of two-dimensional Navier Stokes equation with periodic boundary conditions and incompressible flow

Logan K. Kuiper
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Abstract

An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.

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Logan K. Kuiper. 2016-07-02. Fourier solution of two-dimensional Navier Stokes equation with periodic boundary conditions and incompressible flow. https://arxiv.org/abs/1607.00566

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