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Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics

1
Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary
2
Montavid Thermodynamic Research Group, 1112 Budapest, Hungary
3
Wigner Research Centre for Physics, Department of Theoretical Physics, Institute for Particle and Nuclear Physics, 1525 Budapest, Hungary
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(12), 1376; https://doi.org/10.3390/e22121376
Received: 1 November 2020 / Revised: 25 November 2020 / Accepted: 30 November 2020 / Published: 5 December 2020
(This article belongs to the Section Thermodynamics)
The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions and in the aspect of the virtues of a thermodynamical approach. Regarding the scheme, the arrangement of which quantity is represented where in discretized spacetime, including the question of appropriately realizing the boundary conditions, is nontrivial. In parallel, placing the problem in the thermodynamical framework proves to be beneficial in regards to monitoring and controlling numerical artefacts—instability, dissipation error, and dispersion error. This, in addition to the observed preciseness, speed, and resource-friendliness, makes the thermodynamically extended symplectic approach that is presented here advantageous above commercial finite element software solutions. View Full-Text
Keywords: symplectic numerical methods; rheology; solids; waves; spacetime; thermodynamics symplectic numerical methods; rheology; solids; waves; spacetime; thermodynamics
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MDPI and ACS Style

Pozsár, Á.; Szücs, M.; Kovács, R.; Fülöp, T. Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics. Entropy 2020, 22, 1376. https://doi.org/10.3390/e22121376

AMA Style

Pozsár Á, Szücs M, Kovács R, Fülöp T. Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics. Entropy. 2020; 22(12):1376. https://doi.org/10.3390/e22121376

Chicago/Turabian Style

Pozsár, Áron, Mátyás Szücs, Róbert Kovács, and Tamás Fülöp. 2020. "Four Spacetime Dimensional Simulation of Rheological Waves in Solids and the Merits of Thermodynamics" Entropy 22, no. 12: 1376. https://doi.org/10.3390/e22121376

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