Fully Eulerian fluid–structure interaction for time-dependent problems

A fully Eulerian framework formulation for solving time-dependent fluid–structure interaction problems is proposed in this work. Although some preliminary work on this approach exists for stationary configurations, it remains to validate nonstationary processes. The formulation is stated in an implicit monolithic frame of reference. A finite difference scheme is used for temporal discretization whereas the spatial discretization is based on a Galerkin finite element scheme. The nonlinear problem is solved with a Newton method and with analytical evaluation of the Jacobian matrix. In contrast to interface tracking methods (for example, the arbitrary Lagrangian–Eulerian approach), the interface must be captured, which is similar to the level-set method. Consequently, the interface is allowed to intersect mesh cells, which is a crucial difficulty of this method where appropriate treatment must be suggested. The proposed formulation is substantiated by three numerical tests in which the performance of fully Eulerian fluid–structure interaction is demonstrated.