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An augmented Lagrangian preconditioner for implicitly constituted non-Newtonian incompressible flow. (English) Zbl 1458.65147
The authors are concerned with the construction of a preconditioner for the Newton linearization of a system describing the steady state flow of an implicitly constituted non-Newtonian incompressible fluid. The formulation uses three variables namely, velocity, pressure (mean normal stress) and shear stress and the implicit constitutive relation is of power-law type. The preconditioner is built on a Reynolds-robust preconditioner for the three-dimensional Newtonian system to which the first author contributed. The fundamental idea has been to additionally introduce an augmented Lagrangian term. The preconditioner proved to be robust with respect to variation of the rheological parameters in numerical experiments carried out by authors.
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65F08 Preconditioners for iterative methods
35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
Firedrake; hypre; ML; PETSc
Full Text: DOI
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