A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation
A defect-correction mixed finite element method for solving the time-dependent Johnson-Segalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual i...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/689804 |
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| _version_ | 1850208870768574464 |
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| author | Yunzhang Zhang Yanren Hou Ganshan Yang |
| author_facet | Yunzhang Zhang Yanren Hou Ganshan Yang |
| author_sort | Yunzhang Zhang |
| collection | DOAJ |
| description | A defect-correction mixed finite element method for solving the time-dependent
Johnson-Segalman viscoelastic equations in two dimensions is given. In
the defect step, the constitutive equation is computed with the artificially
reduced Weissenberg parameter for stability, and the resulting residual is
corrected in the correction step on the same grid. A streamline upwind
Petrov-Galerkin (SUPG) approximation is used to stabilize the hyperbolic
character of the constitutive equation for the stress. We establish a priori
error estimates for the defect step and the first correction step of the defect
correction method. The derived theoretical results are supported by
numerical tests. |
| format | Article |
| id | doaj-art-981e4302eb0d4d9fa9ef0c86b0a75453 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-981e4302eb0d4d9fa9ef0c86b0a754532025-08-20T02:10:09ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/689804689804A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG FormulationYunzhang Zhang0Yanren Hou1Ganshan Yang2School of Science, Xi'an Jiaotong University, Xi'an 710049, ChinaSchool of Science, Xi'an Jiaotong University, Xi'an 710049, ChinaInstitute of Mathematics Science, Yunnan Normal University, Kunming 650092, ChinaA defect-correction mixed finite element method for solving the time-dependent Johnson-Segalman viscoelastic equations in two dimensions is given. In the defect step, the constitutive equation is computed with the artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step on the same grid. A streamline upwind Petrov-Galerkin (SUPG) approximation is used to stabilize the hyperbolic character of the constitutive equation for the stress. We establish a priori error estimates for the defect step and the first correction step of the defect correction method. The derived theoretical results are supported by numerical tests.http://dx.doi.org/10.1155/2011/689804 |
| spellingShingle | Yunzhang Zhang Yanren Hou Ganshan Yang A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation Discrete Dynamics in Nature and Society |
| title | A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation |
| title_full | A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation |
| title_fullStr | A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation |
| title_full_unstemmed | A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation |
| title_short | A Defect-Correction Method for Time-Dependent Viscoelastic Fluid Flow Based on SUPG Formulation |
| title_sort | defect correction method for time dependent viscoelastic fluid flow based on supg formulation |
| url | http://dx.doi.org/10.1155/2011/689804 |
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