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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 ease the computatio...

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Autores principales: Fülöp, Tamás, Kovács, Róbert, Szücs, Mátyás, Fawaier, Mohammad
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516568/
https://www.ncbi.nlm.nih.gov/pubmed/33285930
http://dx.doi.org/10.3390/e22020155
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author Fülöp, Tamás
Kovács, Róbert
Szücs, Mátyás
Fawaier, Mohammad
author_facet Fülöp, Tamás
Kovács, Róbert
Szücs, Mátyás
Fawaier, Mohammad
author_sort Fülöp, Tamás
collection PubMed
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.
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spelling pubmed-75165682020-11-09 Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids Fülöp, Tamás Kovács, Róbert Szücs, Mátyás Fawaier, Mohammad Entropy (Basel) Article 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. MDPI 2020-01-28 /pmc/articles/PMC7516568/ /pubmed/33285930 http://dx.doi.org/10.3390/e22020155 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Fülöp, Tamás
Kovács, Róbert
Szücs, Mátyás
Fawaier, Mohammad
Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids
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 Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516568/
https://www.ncbi.nlm.nih.gov/pubmed/33285930
http://dx.doi.org/10.3390/e22020155
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