Time-adaptive partitioned method for fluid-structure interaction problems with thick structures

Abstract

In this paper, we present a partitioned numerical scheme for solving fluid-structure interaction (FSI) problems based on the adaptive time-stepping. The viscous, incompressible fluid is described using the Navier-Stokes equations expressed in an Arbitrary Lagrangian Eulerian (ALE) form while the elastic structure is modeled using elastodynamic equations. We implement a partitioned scheme based on the Robin-Robin coupling conditions at the interface, combined with the refactorization of Cauchy's one-legged θ-like method with adaptive time-stepping. The method is unconditionally stable, and for θ=12, it corresponds to the midpoint rule, which is conservative and second-order convergent in time. The focus of this paper is to study the time-adaptivity properties of the proposed method, and to explore the parameters used in the variable time-stepping. The adaptive process is based on the local truncation error (LTE), for computation of which we consider two methods: Milne's device using a modified Adams-Bashforth two-step method, and Taylor's method. The performance of the method is explored in numerical examples, where the adaptive approach is compared to the one where a fixed time step is used. We present an example based on the method of manufactured solutions, where the effect of different parameters is studied, followed by a classical benchmark problem of a flow around a rigid cylinder attached to a nonlinearly elastic bar inside a two-dimensional channel. Finally, we present a three-dimensional, simplified example of blood flow in a compliant artery.