An augmented Lagrangian approach to simulating yield stress fluid flows around a spherical gas bubble

We simulated the flow of a yield stress fluid around a gas bubble using an augmented Lagrange approach. The piecewise linear equal-order finite elements for both the velocity and the pressure approximations proposed and analyzed by Latche and Vola in 2004 were applied. A mesh adaptive strategy based on this element-pair choice was also proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme was formulated for general HerschelBulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble were provided to validate the proposed algorithm. Copyright (C) 2011 John Wiley & Sons, Ltd.