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

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

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

3 Citations (Scopus)
153 Downloads (Pure)

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
Keetels, G.H. ; Clercx, H.J.H. ; van Heijst, G.J.F. / Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. Computational Science - ICCS 2007. Berlin : Springer, 2007. pp. 898-905 (Lecture Notes in Computer Science; 4487).
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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.",
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Keetels, GH, Clercx, HJH & van Heijst, GJF 2007, Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. in Computational Science - ICCS 2007., 10.1007/978-3-540-72584-8_118, Lecture Notes in Computer Science, no. 4487, vol. 4487, Springer, Berlin, pp. 898-905. https://doi.org/10.1007/978-3-540-72584-8_118

Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. / Keetels, G.H.; Clercx, H.J.H.; van Heijst, G.J.F.

Computational Science - ICCS 2007. Berlin : Springer, 2007. p. 898-905 10.1007/978-3-540-72584-8_118 (Lecture Notes in Computer Science; Vol. 4487, No. 4487).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

T1 - Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization

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N2 - 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.

AB - 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.

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Keetels GH, Clercx HJH, van Heijst GJF. Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization. In Computational Science - ICCS 2007. Berlin: Springer. 2007. p. 898-905. 10.1007/978-3-540-72584-8_118. (Lecture Notes in Computer Science; 4487). https://doi.org/10.1007/978-3-540-72584-8_118