A quantitative evaluation of viscosity regularization in predicting transient flows of viscoplastic fluids

Abstract

Abstract We present an assessment of viscosity regularization (VR) in predicting transient flows of viscoplastic fluids (VPF). Although VR has been the most popular approach for computational studies of VPF in the last decade, the understanding of its effects on the predicted flow behaviour has remained largely qualitative. To reveal the effects of VR, we present a systematic quantitative comparison of the solutions of the regularized and exact (i.e. not regularized) problems. We consider free convection of a Bingham fluid in a two-dimensional square cavity with differentially heated sidewalls. We use bi-viscosity as a representative VR model and use augmented Lagrangian (AL) method to solve the exact problem. We show that common methods of assessing the solution error can hugely overestimate the accuracy of the results of VR. In particular, complete loss of accuracy is observed when flow conditions approach the motionless state, rendering the lower computational cost and algorithmic simplicity of VR irrelevant. Furthermore, we quantify the accuracy of bi-viscosity regularization in predicting the unyielded regions. This analysis disproves by counterexample that using yield stress contours produces convergent numerical estimates of the unyielded regions.