Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization

G.H. Keetels, H.J.H. Clercx, G.J.F. van Heijst

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    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 languageUndefined
    Title of host publicationComputational Science - ICCS 2007
    Place of PublicationBerlin
    PublisherSpringer
    Pages898-905
    Number of pages10
    ISBN (Print)978-3-540-72583-1
    DOIs
    Publication statusPublished - 13 Jul 2007

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer Verlag
    Number4487
    Volume4487

    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