An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow

Abstract

We propose an augmented Lagrangian preconditioner for a three-field stress-velocitypressure discretization of stationary non-Newtonian incompressible flow with an implicit constitutive relation of power-law type. The discretization employed makes use of the divergence-free Scott-Vogelius pair for the velocity and pressure. The preconditioner builds on the work [P. E. Farrell, L. Mitchell, and F. Wechsung, SIAM J. Sci. Comput., 41 (2019), pp. A3073-A3096], where a Reynolds-robust preconditioner for the three-dimensional Newtonian system was introduced. The preconditioner employs a specialized multigrid method for the stress-velocity block that involves a divergence-capturing space decomposition and a custom prolongation operator. The solver exhibits excellent robustness with respect to the parameters arising in the constitutive relation, allowing for the simulation of a wide range of materials.

Recycling augmented Lagrangian preconditioner in an incompressible fluid solver

“…Introduction. Augmented Lagrangian (AL) preconditioning is a potent technique that has been developed to solve some highly non-symmetric algebraic systems having a saddle point structure [2,3,5,12,15,22,23,24,33,40,51]. The need to treat such problems numerically emerges from the discretization of systems of PDEs describing the motion of incompressible viscous fluid with dominating inertia effects.…”