Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method
The newly developed algorithm called the grid-by-grid inversion method is a very convenient method for converting an existing computer code for Newtonian flow simulations to that for viscoelastic flow simulations. In this method, the hyperbolic constitutive equation is split such that the term for t...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/420189 |
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| author | H. M. Park |
| author_facet | H. M. Park |
| author_sort | H. M. Park |
| collection | DOAJ |
| description | The newly developed algorithm called the grid-by-grid inversion method is a very convenient method for converting an existing computer code for Newtonian flow simulations to that for viscoelastic flow simulations. In this method, the hyperbolic constitutive equation is split such that the term for the convective transport of stress tensor is treated as a source which is updated iteratively. This allows the stress tensors at each grid point to be expressed in terms of velocity gradient tensor at the same location, and the set of stress tensor components is found after inverting a small matrix at each grid point. To corroborate the robustness and accuracy of the grid-by-grid inversion method, we apply it to the 4 : 1 axisymmetric contraction problem. This algorithm is found to be robust and yields accurate results as compared with other finite volume methods. Any commercial CFD packages for Newtonian flow simulations can be easily converted to those for viscoelastic fluids exploiting the grid-by-grid inversion method. |
| format | Article |
| id | doaj-art-d46f53924ddf41eda166c79f29be3650 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d46f53924ddf41eda166c79f29be36502025-02-03T01:21:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/420189420189Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion MethodH. M. Park0Department of Chemical and Biomolecular Engineering, Sogang University, Seoul 121-742, Republic of KoreaThe newly developed algorithm called the grid-by-grid inversion method is a very convenient method for converting an existing computer code for Newtonian flow simulations to that for viscoelastic flow simulations. In this method, the hyperbolic constitutive equation is split such that the term for the convective transport of stress tensor is treated as a source which is updated iteratively. This allows the stress tensors at each grid point to be expressed in terms of velocity gradient tensor at the same location, and the set of stress tensor components is found after inverting a small matrix at each grid point. To corroborate the robustness and accuracy of the grid-by-grid inversion method, we apply it to the 4 : 1 axisymmetric contraction problem. This algorithm is found to be robust and yields accurate results as compared with other finite volume methods. Any commercial CFD packages for Newtonian flow simulations can be easily converted to those for viscoelastic fluids exploiting the grid-by-grid inversion method.http://dx.doi.org/10.1155/2012/420189 |
| spellingShingle | H. M. Park Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method Journal of Applied Mathematics |
| title | Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method |
| title_full | Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method |
| title_fullStr | Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method |
| title_full_unstemmed | Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method |
| title_short | Viscoelastic Flow through an Axisymmetric Contraction Using the Grid-by-Grid Inversion Method |
| title_sort | viscoelastic flow through an axisymmetric contraction using the grid by grid inversion method |
| url | http://dx.doi.org/10.1155/2012/420189 |
| work_keys_str_mv | AT hmpark viscoelasticflowthroughanaxisymmetriccontractionusingthegridbygridinversionmethod |