### Abstract

In this study we use a fast Fourier spectral technique to simulate the Navier-Stokes equations with no-slip boundary conditions. This is enforced by an immersed boundary technique called volume-penalization. The approach has been justified by analytical proofs of the convergence with respect to the penalization parameter. However, the solution of the penalized Navier-Stokes equations is not smooth on the surface of the penalized volume. Therefore, it is not a priori known whether it is possible to actually perform accurate fast Fourier spectral computations. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole-wall collision as a test case. It is found that Gibbs oscillations have a negligible effect on the flow evolution. This allows higher-order recovery of the accuracy on a Fourier basis by means of a post-processing procedure.

Original language | Undefined |
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Title of host publication | Computational Science - ICCS 2007 |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 898-905 |

Number of pages | 10 |

ISBN (Print) | 978-3-540-72583-1 |

DOIs | |

Publication status | Published - 13 Jul 2007 |

### Publication series

Name | Lecture Notes in Computer Science |
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Publisher | Springer Verlag |

Number | 4487 |

Volume | 4487 |

### Keywords

- EWI-11814
- IR-64597
- METIS-247042

## Cite this

Keetels, G. H., Clercx, H. J. H., & van Heijst, G. J. F. (2007). Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. In

*Computational Science - ICCS 2007*(pp. 898-905). [10.1007/978-3-540-72584-8_118] (Lecture Notes in Computer Science; Vol. 4487, No. 4487). Berlin: Springer. https://doi.org/10.1007/978-3-540-72584-8_118