The immersed/fictitious element method for fluid-structure interaction: Volumetric consistency, compressibility and thin members

A weak form and an implementation are given for fluid-structure interaction by the immersed/fictitious element method for compressible fluids. The weak form is applicable to models where the fluid is described by Eulerian coordinates while the solid is described by Lagrangian coordinates, which suits their intrinsic characteristics. A unique feature of the method is the treatment of the fictitious fluid by a Lagrangian description, which simplifies the interface conditions. Methods for enforcing volumetric consistency between the fluid and solid and treating thin members are given. Although a compressible viscous fluid is considered here, the new developments can be applied to incompressible fluids.