Strongly coupled partitioned FSI using proper orthogonal decomposition

Abstract

In this paper we present a strong coupling algorithm for partitioned fluid-structure interactions which can be applied to black-box field solvers. The coupling algorithm constructs an approximate interface Jacobian of the coupled fluid-structure problem using proper orthogonal decomposition (POD) reduced order models of the interface tractions and displacements. The coupling scheme is an augmentation of the IBQN-LS (interface block-quasi-Newton with an approximation for the Jacobian from least-squares) coupling scheme. The performance of the original IBQN-LS method is strongly governed by the number of previous time step histories that are retained, where there exists a problem specific optimal choice. In this paper we will demonstrate that this dependence on the number of retained histories is due to a trade-off between increasingly ill-conditioned interface Jacobian, when too many histories are retained and sub-optimal coupling convergence rates due to a loss of information when histories are discarded. We will show that the POD augmentation allows for the reuse of all observations from previous time steps by limiting the matrix ill-conditioning while essentially retaining ‘all’ the information. Retaining all histories improves the approximation of the interface block-Newton Jacobian, which in turn improves the coupling iterations’ convergence rates. We will demonstrate on a flexible tube benchmark problem that once sufficient information has been captured that the POD interface reduced order model can produce near quadratic convergence rates.