A mechanically consistent unified formulation for fluid-porous-structure-contact interaction.

Fluid-structure interaction with contact poses profound mathematical and numerical challenges, particularly when considering realistic contact scenarios and the influence of surface roughness. Computationally, contact introduces challenges in altering the fluid domain topology and preserving stress balance. This work introduces a new mathematical framework for a unified continuum description of fluid-porous-structure-contact interaction (FPSCI), leveraging the Navier-Stokes-Brinkman (NSB) equations to incorporate porous effects within the surface asperities in the contact region. Our approach maintains mechanical consistency during contact, circumventing issues associated with contact models and complex interface coupling conditions, allowing for the modeling of tangential creeping flows due to surface roughness. The unified continuum and variational multiscale formulation ensure robustness by enabling stable and unified integration of fluid, porous, and solid sub-problems. Computational efficiency and ease of implementation - key advantages of our approach - are demonstrated by solving two benchmark problems of a falling ball and an idealized heart valve. This research has broad implications for fields reliant on accurate fluid-structure interactions and promising advancements in modeling and numerical simulation techniques.