Quasi-Newton methods for implicit black-box FSI coupling

In this paper we introduce a new multi-vector update quasi-Newton (MVQN) method for implicit coupling of partitioned, transient FSI solvers. The new quasi-Newton method facilitates the use of ‘black-box’ field solvers and under certain circumstances can be demonstrated to provide Newton-like convergence behaviour for strongly coupled FSI benchmark problems. We demonstrate the superior convergence behaviour and robust nature of the MVQN method compared to other well known quasi-Newton coupling schemes, including the least squares reduced order modelling (IBQN-LS) scheme, the classical rank-1 update Broyden’s method and fixed point iterations with dynamic relaxation. The quasi-Newton methods are analysed on a suite of strongly coupled FSI problems, including but not limited to, internal, incompressible flow through a flexible tube where the solid density is an order of magnitude lower than the fluid density.