  We consider the aeroelastic simulation of flexible mechanical structures
submerged in subsonic fluid flows at low Mach numbers. The nonlinear kinematics
of flexible bodies are described in the total Lagrangian formulation and
discretized by finite elements. The aerodynamic loads are computed using the
unsteady vortex-lattice method wherein a free wake is tracked over time. Each
implicit time step in the dynamic simulation then requires solving a nonlinear
equation system in the structural variables with additional aerodynamic load
terms. Our focus here is on the efficient numerical solution of this system by
accelerating the Newton algorithm. The particular structure of the aeroelastic
nonlinear system suggests the structural derivative as an approximation to the
full derivative in the linear Newton system. We investigate and compare two
promising algorithms based in this approximation, a quasi-Newton type algorithm
and a novel inexact Newton algorithm. Numerical experiments are performed on a
flexible plate and on a wind turbine. Our computational results show that the
approximation can indeed accelerate the Newton algorithm substantially.
Surprisingly, the theoretically preferable inexact Newton algorithm is much
slower than the quasi-Newton algorithm, which motivates further research to
speed up derivative evaluations.
