Paper Info
Title
The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport.
Abstract
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.
Year
DOI
Venue
2016
10.1016/j.jcp.2016.01.013
Journal of Computational Physics
Keywords
Field
DocType
Gibbs phenomenon,Immersed boundary method,Immersed interface,Large eddy simulation,Spectral discretization
Immersed boundary method,Gibbs phenomenon,Discretization,Mathematical optimization,Large eddy simulation,Numerical integration,Scalar (physics),Momentum,Incompressible flow,Physics
Journal
Volume
Issue
ISSN
310
C
0021-9991
Citations 
PageRank 
References 
0
0.34
5
Authors
3
Name
Order
Citations
PageRank
Qi Li111.04
Elie Bou-Zeid221.13
William Anderson300.34