Partitioned but Strongly Coupled Iteration Schemes for Nonlinear Fluid-Structure Interaction

We look at the computational procedure of computing the response of a coupled fluid-structure interaction problem. We use the so called strong fluid-structure coupling --- a totally implicit formulation. At each time step in an implicit formulation, new values for the solution variables have to be computed by solving a nonlinear system of equations, where we assume that we have solvers for the subproblems. This is often the case, when we have existing software to solve each subproblem separately, and want to couple both. We show how to solve the overall nonlinear system by using only the solvers for the subproblems. This is achieved not by considering the equilibrium equations, but the fixed-point problem resulting from the solution iteration for each of the subproblems

Nonlinear Galerkin Methods for the Model Reduction of Nonlinear Dynamical Systems: Revised and expanded version of a contribution to the EUROMECH Coloquium 427, ENS Cachan France, September 2001

Numerical simulations of large nonlinear dynamical systems, especially over long time intervalls, 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 subspace of its phase space. Nonlinear Galerkin methods try to improve on this by projecting onto a submanifold which does not have to be flat. These methods are applied to the finite element model of a windturbine, 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