The flow of viscoelastic fluids past a cylinder: finite-volume high-resolution methods

Abstract

Accurate solutions are obtained with the numerical method of Oliveira et al. [J. Non-Newtonian Fluid Mech. 79 (1998) 1] for the inertialess plane flow around a confined cylinder. This numerical procedure is based on the finite-volume method in non-orthogonal block-structured meshes with a collocated arrangement of the dependent variables, and makes use of a special interpolation practice to avoid stress–velocity decoupling. Two high-resolution schemes (MINMOD and SMART) are implemented to represent the convective terms in the constitutive equations for the upper convected Maxwell and Oldroyd-B fluids, and the resulting predictions of the drag coefficient on the cylinder are shown to be as accurate as existing finite-element method predictions based on the supposedly very accurate h-p refinement technique. Numerical uncertainties are quantified with help of Richardson’s extrapolation technique and the orders of convergence of the differencing schemes are established and shown to be second-order accurate. Calculations performed with a wake-refined mesh predicted the variation of the maximum longitudinal normal stress in the wake as De 3 and De 5 depending on Deborah number.