A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation

A stabilized semi-implicit fractional step finite element method for solving coupled
fluid-structure interaction problems involving free surface waves is presented. The
stabilized governing equations for the viscous incompressible fluid and the free surface
are derived at a differential level via a finite calculus procedure. A mesh updating
technique based on solving a fictitious elastic problem on the moving mesh
is described. Examples of the efficiency of the stabilized semi-implicit algorithm for
the analysis of fluid-structure interaction problems in totally or partially submerged
bodies is presented.