An augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity with piecewise linear equal-order finite elements

摘要

We study an augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity. The piecewise linear equal-order finite element spaces for both the velocity and the pressure approximations, proposed and analyzed by Latche and Vola [18], are applied. Based on the resulting regularity of the numerical solutions, a mesh adaptive strategy is proposed to render the yield surfaces of desired resolution. The corresponding numerical scheme is formulated for general Herschel-Bulkley models, and its validity is verified on the benchmark model: Bingham fluid flows in a lid-driven square cavity.