An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems Original Research Article

This paper is concerned with the fully coupled (‘monolithic’) solution of large-displacement fluid–structure interaction problems by Newton’s method. We show that block-triangular approximations of the Jacobian matrix, obtained by neglecting selected fluid–structure interaction blocks, provide good preconditioners for the solution of the linear systems with GMRES. We present an efficient approximate implementation of the preconditioners, based on a Schur complement approximation for the Navier–Stokes block and the use of multigrid approximations for the solution of the computationally most expensive operations. The performance of the the preconditioners is examined in representative steady and unsteady simulations which show that the GMRES iteration counts only display a mild dependence on the Reynolds number and the mesh size. The final part of the paper demonstrates the importance of consistent stabilisation for the accurate simulation of fluid–structure interaction problems.