A strongly-coupled cell-based smoothed finite element solver for unsteady viscoelastic fluid–structure interaction

Abstract

This paper describes a cell-based smoothed finite element method (CS-FEM) for computing unsteady viscoelastic fluid–structure interaction (VFSI) within the arbitrary Lagrangian–Eulerian framework. The incompressible Navier–Stokes equations incorporating the Oldroyd-B constitutive relation are decoupled via the smoothed characteristic-based split scheme that allows equal low-order interpolations for the triple primitive variables. The elastodynamics equation of a geometrically nonlinear solid is solved by the modified Newton–Raphson method in conjunction with the generalized-α method. Following an efficient moving mesh strategy, the block-Gauss–Seidel procedure is utilized to tightly couple three interacting fields. In particular, CS-FEM is adopted to spatially discretize the global VFSI system where all gradient related terms are readily smoothed. The cell-based smoothing concept is also introduced to evaluate viscoelastic fluid forces acting on the deformable body. Two transient VFSI examples are analyzed to demonstrate the enlarged applicability of CS-FEM. The main characteristics of viscoelastic flow-induced oscillations are successfully captured.