An Interface-Manifold Aware Projection (IMAP) Method: A fast simulation framework that automatically evolves along the no-slip manifold tangent

Modern surface and sub-surface architectures offer a promising paradigm for next-level passive, adaptive flow control. High-fidelity simulation tools that compute the nonlinearly coupled flow-surface interplay are key to enabling this technology. Existing methods often require complex modifications to the flow solvers, such as altering stencils or embedding costly linear solves that can significantly increase the cost compared with body-less solvers. To overcome these challenges, we present IMAP, a novel, non-intrusive simulation framework for complex flow-structure interactions. IMAP's approach is rooted in viewing the no-slip constraint as a manifold within which the flow evolves. The method centers on constructing projections to constrain the dynamics to this manifold before time advancement. These projection steps leverage standard immersed-boundary operators and are built from small, surface-local operators that do not involve large-dimensional linear systems. IMAP eliminates the need for costly embedded solves inherent to many projection-based immersed boundary methods, as well as stencil modifications associated with other immersed boundary/interface methods. We demonstrate the efficacy of the approach on flows past bodies undergoing prescribed kinematics. Future extensions will focus on fully coupled fluid-structure interplay.