Numerical simulation of Fluid–Structure Interaction problems with viscoelastic fluids using a log-conformation reformulation

Abstract

In this paper the numerical simulation of the interaction between Oldroyd-B viscoelastic fluid flows and hyperelastic solids is approached. The algorithm employed is a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially. A Galerkin finite element approach has been employed for the numerical approximation of the solid, while the flow equations are approximated using a stabilized finite element method based on the Variational Multi-Scale approach to overcome the instabilities of the Galerkin method. To be able to deal with flows with dominant elasticity, a log-conformation reformulation of the constitutive equation can be employed; here this approach is extended to Fluid–Structure Interaction problems. Several numerical examples are presented and discussed to assess the robustness of the proposed scheme and its applicability to problems with viscoelastic fluids in which elasticity is dominant interacting with hyperelastic solids.