An augmented Lagrangian approach with enhanced local refinement to simulating yield stress fluid flows around a spherical gas bubble

DOI: 10.5176/2251-1911_CMCGS14.04

Authors: Jianying Zhang

Abstract: We simulate the flow of a yield stress fluid around a gas bubble using an augmented Lagrange approach with piecewise linear equal-order finite elements for both the velocity and the pressure approximations. An enhanced mesh adaptive strategy based on this element-pair choice is also proposed to render the yield surfaces with desired resolution. The corresponding numerical scheme is formulated for general Herschel-Bulkley fluids. Numerical results on Bingham fluid flows around a slowly rising spherical gas bubble are provided to showcase the improvement on the previously proposed algorithm in [12].

Keywords: Viscoplastic fluids, Yield surfaces, Bingham fluid flows, Augmented Lagrange method, Gas bubble dynamics