TY - JOUR
T1 - The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport
AU - Li, Qi
AU - Bou-Zeid, Elie
AU - Anderson, William
N1 - Funding Information:
This study was funded by the US National Science Foundation under Grant CBET-1058027 . The simulations were performed on the supercomputing clusters of the National Center for Atmospheric Research through project P36861020 . W.A. was supported by the Army Research Office Environmental Sciences Directorate (PM: Dr. Sandra Collier; Grant # W911NF-13-1-0474 ).
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - 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.
AB - 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.
KW - Gibbs phenomenon
KW - Immersed boundary method
KW - Immersed interface
KW - Large eddy simulation
KW - Spectral discretization
UR - http://www.scopus.com/inward/record.url?scp=84955248095&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84955248095&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.01.013
DO - 10.1016/j.jcp.2016.01.013
M3 - Article
AN - SCOPUS:84955248095
SN - 0021-9991
VL - 310
SP - 237
EP - 251
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -