Isogeometric fluid–structure interaction analysis with emphasis on non-matching discretizations, and with application to wind turbines

Abstract

In this paper we develop a framework for fluid–structure interaction (FSI) modeling and simulation with emphasis on isogeometric analysis (IGA) and non-matching fluid–structure interface discretizations. We take the augmented Lagrangian approach to FSI as a point of departure. Here the Lagrange multiplier field is defined on the fluid–structure interface and is responsible for coupling of the two subsystems. Thus the FSI formulation does not rely on the continuity of the underlying function spaces across the fluid–structure interface in order to produce the correct coupling conditions between the fluid and structural subdomains. However, in deriving the final FSI formulation the interface Lagrange multiplier is formally eliminated and the formulation is written purely in terms of primal variables. Avoiding the use of Lagrange multipliers adds efficiency to the proposed formulation. As an added benefit, the ability to employ non-matching grids for multi-physics simulations leads to significantly relaxed requirements that are placed on the geometry modeling and meshing tools for IGA.We show an application of the proposed FSI formulation to the simulation of the NREL 5MW offshore wind turbine rotor, where the aerodynamics domain is modeled using volumetric quadratic NURBS, while the rotor structure is modeled using a cubic T-spline-based discretization of a rotation-free Kirchhoff–Love shell. We conclude the article by showing FSI coupling of a T-spline shell with a low-order finite element method (FEM) discretization of the aerodynamics equations. This combined use of IGA and FEM is felt to be a good balance between speed, robustness, and accuracy of FSI simulations for this class of problems.