Numerical simulation of viscoelastic flows with Oldroyd-B constitutive equations and novel algebraic stress models

The purpose of the present study is to compare numerical simulations of viscoelastic flows using the differential Oldroyd-B constitutive equations and two newly devised simplified algebraic explicit stress models (AES-models). The flows of a viscoelastic fluid in a 180° bent planar channel and in a 4:1 planar contraction are considered to illustrate and support the underlying theory. The flow in the bent channel is used to illustrate the frame-invariant property of the new models in a pure shear flow exhibiting strong streamline curvature. The flow in the 4:1 contraction serves as a benchmark test in a situation where strong elongation occurs. For both geometries, it is found that the predictions of the new AES-models are in good agreement with Oldroyd-B up to Deborah numbers of order 0.5, with a significant reduction in computational effort.