Viscous flows in corner regions: Singularities and hidden eigensolutions
Numerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the `moving contact-line problem' and gives...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1797076605452943360 |
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| author | Sprittles, J Shikhmurzaev, Y |
| author_facet | Sprittles, J Shikhmurzaev, Y |
| author_sort | Sprittles, J |
| collection | OXFORD |
| description | Numerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the `moving contact-line problem' and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite-element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh-dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh-independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite element method in the context of the present problem are discussed. |
| first_indexed | 2024-03-07T00:06:05Z |
| format | Journal article |
| id | oxford-uuid:77935687-7f74-4a55-bc3f-bf34c0ba19e9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:06:05Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:77935687-7f74-4a55-bc3f-bf34c0ba19e92022-03-26T20:25:04ZViscous flows in corner regions: Singularities and hidden eigensolutionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:77935687-7f74-4a55-bc3f-bf34c0ba19e9EnglishSymplectic Elements at Oxford2009Sprittles, JShikhmurzaev, YNumerical issues arising in computations of viscous flows in corners formed by a liquid-fluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the `moving contact-line problem' and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite-element method. This modification appears to be insufficient above a certain critical value of the corner angle where the numerical solution becomes mesh-dependent. As shown, this is due to an eigensolution, which exists for all angles and becomes dominant for the supercritical ones. A method of incorporating the eigensolution into the numerical method is described that makes numerical results mesh-independent again. Some implications of the unavoidable finiteness of the mesh size in practical applications of the finite element method in the context of the present problem are discussed. |
| spellingShingle | Sprittles, J Shikhmurzaev, Y Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title | Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title_full | Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title_fullStr | Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title_full_unstemmed | Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title_short | Viscous flows in corner regions: Singularities and hidden eigensolutions |
| title_sort | viscous flows in corner regions singularities and hidden eigensolutions |
| work_keys_str_mv | AT sprittlesj viscousflowsincornerregionssingularitiesandhiddeneigensolutions AT shikhmurzaevy viscousflowsincornerregionssingularitiesandhiddeneigensolutions |