A Fully Eulerian formulation for fluid–structure-interaction problems

► We derive a novel monolithic formulation for fluid structure interactions. ► Fluid and solid problem are given in Eulerian formulation. ► The model can handle: large deformation, contact & topology change. ► We derive a finite element discretization with semi-implicit time-stepping. In this work, we present a Fully Eulerian framework for fluid–structure interaction (fsi) problems coupling the incompressible Navier–Stokes equations with a hyperelastic solid. The Fully Eulerian framework is a monolithic implicit variational formulation for the coupled problem. In contrast to the well-established Arbitrary Lagrangian Eulerian (ALE) coordinates, the Fully Eulerian framework formulates both subproblems, fluid and solid, in Eulerian coordinates. This concept circumvents various difficulties connected to ALE coordinates since no artificial domain mapping is used. The formulation is an interface-capturing method and uses an extension of the solid’s deformation, the Initial Point Set, to detect the interface location. By construction, very large deformation as well as topology changes like contact of the solid to the domain boundary or other solid parts are possible.