Stabilization of a smoothed finite element semi-implicit coupling scheme for viscoelastic fluid–structure interaction

Abstract

We propose in this work a stabilization approach for semi-implicit coupling of viscoelastic fluid–structure interaction (VFSI) using the cell-based smoothed finite element method (CS-FEM). The viscoelastic fluid and nonlinear solid equations are spatially discretized by the CS-FEM and then are semi-implicitly coupled via a partitioned solution strategy. The current semi-implicit coupling framework depends on a second-order characteristic-based split (CBS(B)) scheme that solves the Navier–Stokes equations together with the Oldroyd-B constitutive model in the fractional-step manner. To enhance the stability of the semi-implicit coupling algorithm, the discrete elastic-viscous split stress-gradient (DEVSS-G) procedure is introduced into the explicit stage while the stabilized pressure gradient projection (SPGP) is earmarked for the implicit stage. Moreover, the iterated end-of-step velocity begins with the intermediate velocity during the subiterations. The DEVSS-G/CBS(B)-SPGP technique is readily applied to the CBS-based partitioned semi-implicit coupling algorithm for VFSI. Visible improvements in stabilization and efficiency are revealed in a benchmark test. • A semi-implicit coupling scheme is proposed for viscoelastic fluid–structure interaction. • DEVSS-G/CBS(B)-SPGP stabilization is presented for the semi-implicit scheme. • VFSI system is entirely formulated by cell-based smoothed finite element method. • The developed technique boosts the stability and efficiency considerably.