The log-conformation tensor approach in the finite-volume method framework

Abstract

The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid Mech. 123 (2004) 281], has helped to provide further insights into the High-Weissenberg Number Problem. In this work, we investigate the performance of the log-conformation formulation in the Finite Volume Method (FVM) framework for creeping flows of viscoelastic fluids in steady and unsteady flows around a confined cylinder. The Oldroyd-B and Phan-Thien-Tanner (PTT) constitutive equations were used to assess the effect of different theological behaviour on the flow patterns and solution stability. The calculation of the polymer stress contribution is carried out with both the standard technique and with the log-conformation methodology. For all test cases, up to the critical conditions when both methods converge to a steady solution, the use of the log-conformation technique provides solutions with similar accuracy as the standard approach. In terms of stability the log-conformation formulation is found to be significantly more robust, and Solutions could be obtained at higher Deborah number flows.