Three-dimensional numerical simulation of viscoelastic flow through an abrupt contraction geometry

A numerical scheme for simulating three-dimensional viscoelastic flow was developed. The three-dimensional finite volume method (FVM) based on a non-staggered grid and the semi-implicit method for pressure-linked equations (SIMPLE) were adopted to solve the continuity and momentum equations. As we used a non-staggered grid, the momentum interpolation method (MIM) was employed to avoid checkerboard type pressure fields. Viscoelastic properties of the fluid were described by the Phan-Thien and Tanner (PTT) model, which was treated by the compressive interface capturing scheme for arbitrary meshes (CICSAM). The elastic viscous split stress scheme (EVSS) was used to decouple the velocity and the stress fields. Algebraic equations obtained by the above schemes were handled by an iterative solver and a multi-grid method was applied to accelerate convergence. In order to verify the scheme developed in this study, Newtonian flow in a rectangular duct was studied and the resulting velocity fields were compared with the analytical flow fields. Then viscoelastic flow in 4:1 contraction geometry, one of the most frequently used benchmarking problems, was predicted by applying the fully three-dimensional finite volume method.