A stable second-order scheme for fluid–structure interaction with strong added-mass effects

Abstract

In this paper, we present a stable second-order time accurate scheme for solving fluid–structure interaction problems. The scheme uses so-called Combined Field with Explicit Interface (CFEI) advancing formulation based on the Arbitrary Lagrangian–Eulerian approach with finite element procedure. Although loosely-coupled partitioned schemes are often popular choices for simulating FSI problems, these schemes may suffer from inherent instability at low structure to fluid density ratios. We show that our second-order scheme is stable for any mass density ratio and hence is able to handle strong added-mass effects. Energy-based stability proof relies heavily on the connections among extrapolation formula, trapezoidal scheme for second-order equation, and backward difference method for first-order equation.Numerical accuracy and stability of the scheme is assessed with the aid of two-dimensional fluid–structure interaction problems of increasing complexity. We confirm second-order temporal accuracy by numerical experiments on an elastic semi-circular cylinder problem. We verify the accuracy of coupled solutions with respect to the benchmark solutions of a cylinder-elastic bar and the Navier–Stokes flow system. To study the stability of the proposed scheme for strong added-mass effects, we present new results using the combined field formulation for flexible flapping motion of a thin-membrane structure with low mass ratio and strong added-mass effects in a uniform axial flow. Using a systematic series of fluid–structure simulations, a detailed analysis of the coupled response as a function of mass ratio for the case of very low bending rigidity has been presented.