An unstructured element based finite volume formulation for modeling viscoelastic flow

Abstract

This work presents an element based finite volume methodology (EbFVM) [11] for solving two-dimensional viscoelastic fluid flows. The method can easily deal with hybrid unstructured meshes consisting of both triangular and quadrilateral elements, which allows the discretization of complex geometries. To overcome the problem of partial decoupling of pressure and velocity fields due to the use of a collocated arrangement of variables, it is used a interpolation function of the FIELDS type. Such a function also promoted the inclusion of pressure and stresses in the mass conservation equation improving conditioning of the coefficient matrix of the system of discretized equations. The advection terms in the constitutive equations are approximated using the single point upwind scheme. For testing different aspects of the numerical solution two classic benchmark problems were solved: flow between fixed parallel plates, and 4:1 planar contraction flow.