Simulation of thin elastic solids in the incompressible viscous flow using implicit interface representation

Abstract

This thesis provides a numerical algorithm to solve fluid-structure interaction problems in the Cartesian grid. Unlike the typical Immersed Interfaced Method (IIM), we define thin non-stretchable solid interface with the Level Set function. In addition, we developed a partial differential equation which represents the bending rigidity of the interface. The interface is assumed very thin and has zero elastic stress when it is flat. The interface gives singular forces to the incompressible viscous fluid and the fluid solver handles discontinuities across the interface. Instead of solving two dynamic systems (i.e., fluid and solid), we solve the fluid field only and solve a convection equation of interface with the local fluid velocity. This idea is valid because of viscous fluid (i.e., velocity is continuous across the interface) as we can see frequently in the IIM. The result shows that elastic interface vibrates and converges to an equilibrium state. The oscillatory motion of the interface depends on the viscosity of fluid, Young's modulus and thickness of interface. The results looks correct physically, and they match with the existing IIM results.