Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin and Removal
We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable sing...
| Main Authors: | , |
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| Format: | Journal article |
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2009
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| _version_ | 1797067789277593600 |
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| author | Sprittles, J Shikhmurzaev, Y |
| author_facet | Sprittles, J Shikhmurzaev, Y |
| author_sort | Sprittles, J |
| collection | OXFORD |
| description | We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable singularities in the distribution of the fluid's pressure. The origin of this difficulty is that, near a corner formed by smooth parts of the piece-wise smooth boundary, in addition to the solution of the inhomogeneous problem, there is also an eigensolution. For obtuse corner angles this eigensolution (a) becomes dominant and (b) has a singular radial derivative of velocity at the corner. A method is developed that uses the knowledge about the eigensolution to remove multivaluedness and nonintegrability of the pressure. The method is first explained in the simple case of a Stokes flow in a corner region and then generalised for the full-scale unsteady Navier-Stokes flow in a domain with a free surface. |
| first_indexed | 2024-03-06T22:01:22Z |
| format | Journal article |
| id | oxford-uuid:4eb535b8-e8ba-41ba-8540-82679bbffc22 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:01:22Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:4eb535b8-e8ba-41ba-8540-82679bbffc222022-03-26T16:02:46ZViscous Flow in Domains with Corners: Numerical Artifacts, their Origin and RemovalJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4eb535b8-e8ba-41ba-8540-82679bbffc22Symplectic Elements at Oxford2009Sprittles, JShikhmurzaev, YWe show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable singularities in the distribution of the fluid's pressure. The origin of this difficulty is that, near a corner formed by smooth parts of the piece-wise smooth boundary, in addition to the solution of the inhomogeneous problem, there is also an eigensolution. For obtuse corner angles this eigensolution (a) becomes dominant and (b) has a singular radial derivative of velocity at the corner. A method is developed that uses the knowledge about the eigensolution to remove multivaluedness and nonintegrability of the pressure. The method is first explained in the simple case of a Stokes flow in a corner region and then generalised for the full-scale unsteady Navier-Stokes flow in a domain with a free surface. |
| spellingShingle | Sprittles, J Shikhmurzaev, Y Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin and Removal |
| title | Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin
and Removal |
| title_full | Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin
and Removal |
| title_fullStr | Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin
and Removal |
| title_full_unstemmed | Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin
and Removal |
| title_short | Viscous Flow in Domains with Corners: Numerical Artifacts, their Origin
and Removal |
| title_sort | viscous flow in domains with corners numerical artifacts their origin and removal |
| work_keys_str_mv | AT sprittlesj viscousflowindomainswithcornersnumericalartifactstheiroriginandremoval AT shikhmurzaevy viscousflowindomainswithcornersnumericalartifactstheiroriginandremoval |