The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport

Qi Li, Elie Bou-Zeid, William Anderson

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


Spectral discretization of quantities exhibiting abrupt shifts results in oscillations, or "ringing", known as the Gibbs phenomenon. When spectral discretization is used to evaluate spatial gradients during numerical integration of the transport equations governing turbulent fluid flows, these oscillations can contaminate various flow quantities. A particularly relevant application where the emergence of Gibbs phenomenon is a well-recognized weakness is in the context of simulations using the immersed boundary method. In this paper, we examine the effect of the Gibbs phenomenon in such simulations in detail, and we propose a computationally efficient smoothing treatment to reduce the associated oscillations. The effectiveness of this treatment is demonstrated in a priori tests on functions with abrupt shifts, and in a posteriori tests in wall-modeled large-eddy simulations of incompressible flow and passive scalar transport over solid bluff bodies. Furthermore, the large eddy simulation results indicate that the Gibbs phenomenon's impacts are significantly more detrimental to the computations of the subgrid-scale quantities and of scalar transport close to the solid interface, as compared to their impact on computations involving the resolved velocity field.

Original languageEnglish (US)
Pages (from-to)237-251
Number of pages15
JournalJournal of Computational Physics
StatePublished - Apr 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Gibbs phenomenon
  • Immersed boundary method
  • Immersed interface
  • Large eddy simulation
  • Spectral discretization


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