A coupled two-level set and volume-of-fluid method to simulate fluid-structure interaction of an elastic membrane in a viscous fluid

This work presents a fully Eulerian approach to simulate a cylindrical fluid-membrane interaction. The approach is named the coupled two-level set and volume-of-fluid (C2LSVOF) method owing to its use of the volume-of-fluid (VOF) method to enforce mass conservation, and two-level set (LS) functions to determine the interface shape and the elastic membrane forces. The spatio-temporal flow field is discretized by a single-field, finite difference formulation of incompressible, immiscible Navier-Stokes equations on a stationary grid. The second-order operator split method is used to advect the volume fraction and level set functions by alternating the starting sweep direction at each time step. One level set is advected without implementing the reinitialization algorithm so that its gradient, which can be directly related to the membrane stretching, can be preserved. We apply this approach to benchmark problems involving modeling the large deformation of a flexible elastic membrane in viscous incompressible fluids on each side of the membrane with different density and viscosity ratios. The findings are validated using a stretched and pressurized membrane immersed in a test fluid.