Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

Jiannong Fang, Marc Diebold, Chad Higgins, Marc B. Parlange

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It is known that, when the immersed boundary method (IBM) is implemented within spectral-like methods, the Gibbs oscillation seriously deteriorates the calculation of derivatives near the body surface. In this paper, a radial basis function (RBF) based smoothing technique is proposed with the intention of eliminating or efficiently reducing the Gibbs oscillation without affecting the flow field outside the body. Based on this technique, a combined IBM/spectral scheme is developed to solve the incompressible Navier-Stokes equations. Numerical simulations of flow through a periodic lattice of cylinders of various cross sections are performed. The results demonstrate that the proposed methodology is able to give accurate and nearly oscillation-free numerical solutions of incompressible viscous flows.

Original languageEnglish
Pages (from-to)8179-8191
Number of pages13
JournalJournal of Computational Physics
Issue number22
Publication statusPublished - 10 Sep 2011
Externally publishedYes


  • Gibbs oscillation
  • Immersed boundary method
  • Incompressible viscous flow
  • Navier-Stokes equations
  • Projection method
  • Radial basis function
  • Spectral method

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