Modelling of Bingham and Herschel–Bulkley flows with mixed P1/P1 finite elements stabilized with orthogonal subgrid scale

Published in Journal of Non-Newtonian Fluid Mechanics Vol. 228, pp. 1-16, 2016
doi: 10.1016/j.jnnfm.2015.12.005

Abstract

This paper presents the application of a stabilized mixed pressure/velocity finite element formulation to the solution of viscoplastic non-Newtonian flows. Both Bingham and Herschel–Bulkley models are considered.

The detail of the discretization procedure is presented and the Orthogonal Subgrid Scale (OSS) stabilization technique is introduced to allow for the use of equal order interpolations in a consistent way. The matrix form of the problem is given.

A series of examples is presented to assess the accuracy of the method by comparison with the results obtained by other authors. The extrusion in a Bingham fluid and the movement of a moving and rotating cylinder are analyzed in detail. The evolution of the streamlines, the yielded and unyielded regions, the drag and lift forces are presented.

These benchmark examples show the capacity of the mixed OSS formulation to reproduce the behavior of a Bingham and Herschel–Bulkley flows with the required accuracy.