An Immersed Interface Method for Incompressible Flows and Near Contact

Abstract: We present an enhanced immersed interface method for simulating incompressible fluid flows in thin gaps between closely spaced immersed boundaries. This regime, common in engineered structures such as including tribological interfaces and bearing assemblies, poses significant computational challenges because of limitations in grid resolution and the prohibitive cost of mesh refinement near contact. The immersed interface method imposes jump conditions that capture stress discontinuities generated by forces that are concentrated along immersed boundaries. Our approach introduces a bilinear velocity interpolation operator that incorporates jump conditions from multiple nearby interfaces when they occupy the same interpolation stencil. Numerical results demonstrate substantial improvements in both interface and Eulerian velocity accuracy compared to lubrication-based immersed boundary and immersed interface methods. The proposed method improves upon previous interpolation schemes, and eliminates the need for prior knowledge of interface orientation or geometry. This makes it broadly applicable to a wide range of fluid--structure interaction problems involving near-contact dynamics.