A preconditioner for the steady-state Navier-Stokes equations
We present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier-Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner through...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2002
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| _version_ | 1826300600735760384 |
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| author | Kay, D Loghin, D Wathen, A |
| author_facet | Kay, D Loghin, D Wathen, A |
| author_sort | Kay, D |
| collection | OXFORD |
| description | We present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier-Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the Oseen operator. The preconditioner may also be conceived through a weaker heuristic argument involving differential operators. Computations indicate that convergence for the preconditioned discrete Oseen problem is only mildly dependent on the viscosity (inverse Reynolds number) and, most importantly, that the number of iterations does not grow as the mesh size is reduced. Indeed, since the preconditioner is motivated through analysis of continuous operators, the number of iterations decreases for smaller mesh size which accords with better approximation of these operators. |
| first_indexed | 2024-03-07T05:19:39Z |
| format | Journal article |
| id | oxford-uuid:de6d2815-6bdb-4926-9edc-320a5d6ad13d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:19:39Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:de6d2815-6bdb-4926-9edc-320a5d6ad13d2022-03-27T09:32:13ZA preconditioner for the steady-state Navier-Stokes equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:de6d2815-6bdb-4926-9edc-320a5d6ad13dEnglishSymplectic Elements at Oxford2002Kay, DLoghin, DWathen, AWe present a new method for solving the sparse linear system of equations arising from the discretization of the linearized steady-state Navier-Stokes equations (also known as the Oseen equations). The solver is an iterative method of Krylov subspace type for which we devise a preconditioner through a heuristic argument based on the fundamental solution tensor for the Oseen operator. The preconditioner may also be conceived through a weaker heuristic argument involving differential operators. Computations indicate that convergence for the preconditioned discrete Oseen problem is only mildly dependent on the viscosity (inverse Reynolds number) and, most importantly, that the number of iterations does not grow as the mesh size is reduced. Indeed, since the preconditioner is motivated through analysis of continuous operators, the number of iterations decreases for smaller mesh size which accords with better approximation of these operators. |
| spellingShingle | Kay, D Loghin, D Wathen, A A preconditioner for the steady-state Navier-Stokes equations |
| title | A preconditioner for the steady-state Navier-Stokes equations |
| title_full | A preconditioner for the steady-state Navier-Stokes equations |
| title_fullStr | A preconditioner for the steady-state Navier-Stokes equations |
| title_full_unstemmed | A preconditioner for the steady-state Navier-Stokes equations |
| title_short | A preconditioner for the steady-state Navier-Stokes equations |
| title_sort | preconditioner for the steady state navier stokes equations |
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