NSF-Funded Project (2016-2018)

Fluid-structure interaction with the Navier slip boundary condition



In fluid mechanics the widely accepted boundary condition for viscous flows is the no-slip condition. When applied to fluid-structure interaction (FSI) problems this condition states that the fluid velocity at the moving boundary is equal to the velocity of the boundary itself. If the boundary is rigid and fixed, the no-slip condition states that the fluid velocity at the boundary is zero. This condition is justified only when molecular viscosity is considered. Navier claimed that there should be a slip, and that the slip velocity should be proportional to shear stress. Indeed, kinetic theory calculations have confirmed the Navier slip condition, but they gave the slip length proportional to the mean free path divided by the continuum length, which for practical purposes means zero slip length, justifying the use of no-slip condition. However, recent advances in technology, biomedical engineering, mathematical analysis and scientific computing have re-iterated the need for further studies involving slip boundary conditions. Indeed, it has been recently shown that the no-slip condition is not adequate to model contact between smooth rigid bodies immersed in an incompressible, viscous fluid since contact in such scenarios is not possible. A resolution to this no-collision paradox is to employ a different boundary condition, such as the Navier slip boundary condition, which allows contact between smooth rigid bodies. Additional examples where the Navier slip boundary condition is necessary to capture the ``correct'' physics include the flow of incompressible, viscous fluids over rough boundaries, and fluid flows over hydrophobic surfaces (e.g., spray fabricated liquid repellent surfaces). No mathematical results exist so far that would provide information about the existence of solutions to fluid-structure interaction problems involving incompressible, viscous fluids interacting with elastic/viscoelastic structures via the Navier slip boundary condition. This project focuses on the development of the mathematical theory for fluid-structure interaction problems involving the Navier slip boundary condition. The main goals are to: (1) study existence and well-posedness of FSI problems with the Navier slip condition involving incompressible, viscous fluids, (2) develop a loosely-coupled partitioned scheme for the numerical solution of this class of problems, and (3) apply the knowledge gained from the mathematical theory onto solving real-life problems.



  • Yifan Wang, Postdoctoral Associate, University of Houston
  • Martina Bukac, Faculty, The University of Notre Dame
  • Boris Muha, Faculty, The University of Zagreb


  • Acara Turner, Undergraduate Student, University of Houston
  • Prajakta Bedekar, PhD Student, University of Houston
  • Marija Galic, PhD Student, University of Zagreb


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