Simulation of flow around a thin, flexible obstruction by means of a deforming grid overlapping a fixed grid

This paper presents a numerical method for simulation of coupled flows, in which the fluid interacts with a thin deformable solid, such as flows in cardiovascular valves. The proposed method employs an arbitrary Lagrangian-Eulerian (ALE) method for flow near the solid, embodied in the outflow domain in which the mesh is fixed. The method was tested by modelling a two-dimensional channel flow with a neo-Hookean obstacle, an idealization of the coupled flow near a cardiovascular valve. The effects of the Reynolds number and the dimensionless elastic modulus of the material on the wall shear stress, the size of the downstream reverse flows, and the velocity and pressure profiles were investigated. The deformation of the obstacle, the pressure drop across the obstacle, and the size of the top reverse flow increased as the Reynolds number increased. Conversely, increasing the elastic modulus of the obstacle decreased the deformation of the obstacle and the size qf the top reverse flows, but did not affect the pressure drop across the obstacle over the range studied.