Numerical procedure with analytic derivative for unsteady fluid–structure interaction

The unsteady interaction between an incompressible fluid and a deformable elastic structure is analyzed. An implicit numerical method is proposed. At each time step, the stresses at the fluid–structure interface are determined as a solution of an optimization problem. The modal decomposition of the structure equations leads to a problem to be solved with a reduced number of unknowns. The analytic gradient of the cost function was derived. Numerical tests validate the analytic derivative and show the behavior of a two-dimensional Navier–Stokes equations with plate-like model interaction. Copyright © 2007 John Wiley & Sons, Ltd.