Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 ll-recognized akness is in the context of simulations using the immersed boundary method. ,  examine the effect of the Gibbs phenomenon in such simulations in detail, and  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.
['Qi Li', 'Elie Bou-Zeid', 'William Anderson']
I am writing a research paper on a idea The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport
[{"from": "human", "value": "I am writing a research paper on a idea The impact and treatment of the Gibbs phenomenon in immersed boundary method simulations of momentum and scalar transport"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 ll-recognized akness is in the context of simulations using the immersed boundary method. ,  examine the effect of the Gibbs phenomenon in such simulations in detail, and  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."}]