Using a non-conforming meshes method to simulate an interaction be-tween incompressible flow and rigid and elastic boundaries

Abstract

The interaction between incompressible fluids and elastic and rigid boundaries is seen in many medical, engineering and natural issues. The immersed interface method is used as a non-conforming meshes method to simulate such problems. In this method, the effect of the presence of a body immersed in a fluid is considered by adding a force term to the Navier-Stokes equations. An important advantage of this method is that there is no compulsion to adapt the fluid grids and the boundary grids. First, the flow around a circular cylinder was simulated. As the Reynolds number rises, the vortex dimensions become larger and, as a result, the separation angle of the flow increases. Also, with the Reynolds number increasing, the drag coefficient decreases and the Strouhal number increases and the flow separated from cylinder and two symmetrical vortices is generated behind the cylinder. Then, the behavior of an elastic boundary in shear flow was investigated. It was observed that by increasing bending modulus (increasing stiffness) of body the shape change of the boundary decreases. As well as the tank-treading motion is also observed that this type of movement has been confirmed in experiments.Also observed that the sick cell makes smaller defor-mation, while the normal cell is more deformed and easier passes  the stenosis. This results in reduction of the flow rate in stenosis.This behavior is caused by a type of dis-ease called sickle cell anemia.