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arXiv · 2005.03150

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

P. E. Farrell·P. A. Gazca-Orozco
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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.

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P. E. Farrell, P. A. Gazca-Orozco. 2020-05-06. An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow. https://arxiv.org/abs/2005.03150

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