English

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

Numerical Analysis 2020-08-11 v2 Numerical Analysis

Abstract

We propose an augmented Lagrangian preconditioner for a three-field stress-velocity-pressure 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.

Keywords

Cite

@article{arxiv.2005.03150,
  title  = {An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow},
  author = {P. E. Farrell and P. A. Gazca-Orozco},
  journal= {arXiv preprint arXiv:2005.03150},
  year   = {2020}
}

Comments

To appear in the SIAM Journal on Scientific Computing

R2 v1 2026-06-23T15:22:07.132Z