Towards an efficient immersed boundary projection method for wall-bounded flows with complex surface and sub-surface structures

High-fidelity simulation tools that can predict the fully coupled dynamics between wall-bounded turbulent flows and advanced structures will play a key role in understanding the fluid-metamaterial interaction (FMI) and developing design paradigms that utilize these structures in effective passive flow control. Immersed boundary methods are a natural choice to couple the flow-metamaterial interplay, as these approaches do not require complex body-conforming meshes that would have to adapt in time as the structure moved. In this vein, we present an immersed boundary projection framework that facilitates the simulation of these complex FMI dynamics. We focus on novel features of our formulation, including a new and versatile time stepping methodology based on a Runge-Kutta Chebyshev treatment of stiff viscous terms. Results of this novel formulation will be presented for validation and to demonstrate its potential for complex FMI flows of interest.