An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow
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...
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2020
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| _version_ | 1797085288720236544 |
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| author | Farrell, P |
| author_facet | Farrell, P |
| author_sort | Farrell, P |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T02:06:48Z |
| format | Journal article |
| id | oxford-uuid:9f465e54-6ec7-4300-b41f-7b7069bbd373 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:06:48Z |
| publishDate | 2020 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:9f465e54-6ec7-4300-b41f-7b7069bbd3732022-03-27T00:56:25ZAn augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flowJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9f465e54-6ec7-4300-b41f-7b7069bbd373EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2020Farrell, PWe 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. |
| spellingShingle | Farrell, P An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title | An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title_full | An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title_fullStr | An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title_full_unstemmed | An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title_short | An augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow |
| title_sort | augmented lagrangian preconditioner for implicitly constituted non newtonian incompressible flow |
| work_keys_str_mv | AT farrellp anaugmentedlagrangianpreconditionerforimplicitlyconstitutednonnewtonianincompressibleflow AT farrellp augmentedlagrangianpreconditionerforimplicitlyconstitutednonnewtonianincompressibleflow |