An Enhanced Mesh Refinement Strategy to Capture yield Surfaces around a Spherical Gas Bubble

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 of 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 [1].