Fluid–structure interaction for non-conforming interfaces based on a dual mortar formulation

In the present work the problem of fluid–structure interaction (FSI) with independently space discretized fluid and structure fields is addressed in the context of finite elements. To be able to deal with non-conforming meshes at the fluid–structure interface, we propose the integration of a dual mortar method into the general FSI framework. This method has lately been used successfully to impose interface constraints in other contexts such as finite deformation contact. The main focus is set on monolithic coupling algorithms for FSI here. In these cases the dual mortar approach allows for the elimination of the additional Lagrange multiplier degrees of freedom from the global system by condensation. The resulting system matrices have the same block structure as their counterparts for the conforming case and permit the same numerical treatment. Partitioned Dirichlet–Neumann coupling is also considered briefly and it is shown that the dual mortar approach permits a numerically efficient mapping between fluid and structure quantities at the interface.Numerical examples demonstrate the efficiency and robustness of the proposed method. We present results for a variety of different element formulations for the fluid and the structure field, indicating that the proposed method is not limited to any specific formulation. Furthermore, the applicability of state-of-the-art iterative solvers is considered and the convergence behavior is shown to be comparable to standard simulations with conforming discretizations at the interface.

► We present a fluid–structure interaction framework for non-conforming meshes.
► Dual mortar based method handles additional complexity at very low numerical cost.
► New approach can be advantageous for both monolithic and partitioned FSI.
► The monolithic linear system has same block structure as in the conforming case.
► Numerical efficiency, robustness and scalability for parallel FSI simulations.