A fast, versatile tool for turbulent flow with complex surface behaviors: an immersed boundary-enriched resolvent framework

New structural behaviors via metamaterial architectures offer compelling opportunities for passive, adaptive flow control. A fast and accurate design tool is needed to compute the flow-structure interplay and quantify its dependence on design parameters. Resolvent analysis is a workhorse tool for rapid identification of key flow structures in turbulent flows, yet its current implementation does not allow a versatile treatment of the novel surface behaviors associated with metamaterials. We endow the resolvent analysis framework with an immersed boundary (IB) formalism to address that limitation. Several key scientific questions regarding nonlinear coupling and appropriate norms, given surface motion incorporation into the state variable, arise. Nonlinear coupling of the IB source terms is handled with a formal linearization and Fourier/Laplace transform. We then define the resolvent norm through a rigorously defined energy-based flow-structure norm. Validation will be performed through literature test cases. Results will allow for future work in incorporating various phononic metamaterials with a new outlook on how to probe the coupled response and in identifying key parameters for design applications.