Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids
On the example of the Poynting−Thomson−Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/2/155 |
| _version_ | 1798005025573699584 |
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| author | Tamás Fülöp Róbert Kovács Mátyás Szücs Mohammad Fawaier |
| author_facet | Tamás Fülöp Róbert Kovács Mátyás Szücs Mohammad Fawaier |
| author_sort | Tamás Fülöp |
| collection | DOAJ |
| description | On the example of the Poynting−Thomson−Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling. |
| first_indexed | 2024-04-11T12:32:34Z |
| format | Article |
| id | doaj.art-b4b40534cc8549f6a4c2a7680a37bdc6 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T12:32:34Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-b4b40534cc8549f6a4c2a7680a37bdc62022-12-22T04:23:42ZengMDPI AGEntropy1099-43002020-01-0122215510.3390/e22020155e22020155Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in SolidsTamás Fülöp0Róbert Kovács1Mátyás Szücs2Mohammad Fawaier3Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, HungaryDepartment of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, HungaryDepartment of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, HungaryDepartment of Building Service and Process Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, HungaryOn the example of the Poynting−Thomson−Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling.https://www.mdpi.com/1099-4300/22/2/155symplectic numerical methodsrheologysolidswaves |
| spellingShingle | Tamás Fülöp Róbert Kovács Mátyás Szücs Mohammad Fawaier Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids Entropy symplectic numerical methods rheology solids waves |
| title | Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids |
| title_full | Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids |
| title_fullStr | Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids |
| title_full_unstemmed | Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids |
| title_short | Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids |
| title_sort | thermodynamical extension of a symplectic numerical scheme with half space and time shifts demonstrated on rheological waves in solids |
| topic | symplectic numerical methods rheology solids waves |
| url | https://www.mdpi.com/1099-4300/22/2/155 |
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