Projection-based reduction of fluid–structure interaction systems using monolithic space-time modes

Abstract

The focus of this work is the development of reduced models for engineering applications in complex bidirectional fluid–structure interaction. In the simultaneous solution procedure, velocity variables are used for both fluid and solid, and the whole set of model equations is discretized by a stabilized time-discontinuous space-time finite element method. Flexible structures are modeled using a three-dimensional continuum approach in a total Lagrangian setting considering large displacements and rotations. In the flow domain the incompressible Navier–Stokes equations describe the Newtonian fluid. A continuous finite element mesh is applied to the entire spatial domain, and the discretized model equations are assembled in a single set of algebraic equations, considering the two-field problem as a whole. The continuous fluid–structure mesh with identical orders of approximation for both solid and fluid in space and time automatically yields conservation of mass, momentum and energy at the fluid–structure interface. A mesh-moving scheme is used to adapt the nodal coordinates of the fluid space-time finite element mesh to the structural deformation. The computational approach for strongly coupled fluid–structure interaction is used to create suitable reduced models of generic nonlinear problems. Reduction is performed with monolithic projection-based space-time modes, ensuring strong coupling of fluid and structure in the reduced model. The contribution discusses results using proper orthogonal decomposition (POD) for determination of monolithic space-time modes in the reduction of fluid–structure systems.