Nonlinear Galerkin methods for the model reduction of nonlinear dynamical systems

Numerical simulations of large nonlinear dynamical systems, especially over long-time intervals, may be computationally very expensive. Model reduction methods have been used in this context for a long time, usually projecting the dynamical system onto a sub-space of its phase space. Nonlinear Galerkin methods try to improve on this by projecting onto a sub-manifold which does not have to be flat. These methods are applied to the finite element model of a wind-turbine, where both the mechanical and the aerodynamical degrees of freedom can be considered for model reduction. For the internal forces (moments, section forces) the nonlinear Galerkin method gives a considerable increase in accuracy for very little computational cost.