Unconditionally Stable Pressure-Correction Schemes for a Linear Fluid-Structure Interaction Problem

We consider in this paper numerical approximation of the linear Fluid-Structure Interaction (FSI). We construct a new class of pressure-correction schemesfor the linear FSI problem with a fixed interface, and prove rigorously that theyare unconditionally stable. These schemes are computationally very efficient, asthey lead to, at each time step, a coupled linear elliptic system for the velocity anddisplacement in the whole region and a discrete Poisson equation in the fluid region.