A monolithic approach to fluid–structure interaction using space–time finite elements

Abstract

The paper presents a simultaneous solution procedure for fluid–structure interaction problems. The structural motion is described by geometrically nonlinear elastodynamics. The fluid is modeled by the incompressible Navier–Stokes equations. The space–time finite element method is applied to both continua leading to an almost uniform discretization in which velocity variables are used for fluid and structure. In order to enforce momentum conservation and geometric continuity at the interface, a weighted residual formulation of coupling conditions is introduced. The discretized model equations for fluid, structure and coupling conditions are formulated in a single equation system. The nonlinear system and the fluid mesh movement are solved in a single iteration loop. Two-dimensional examples of membrane flutter and vortex excited plate vibrations demonstrate the efficiency of the methodology.