乐胖代购免代理版

{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:56:18Z","timestamp":1740149778616,"version":"3.37.3"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,28]],"date-time":"2020-01-28T00:00:00Z","timestamp":1580169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011019","name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","doi-asserted-by":"publisher","award":["116375","116197","KH 130378","K124366(124508)"],"id":[{"id":"10.13039\/501100011019","id-type":"DOI","asserted-by":"publisher"}]},{"name":"FIEK","award":["16-1-2016-0007"]},{"name":"Higher Education Excellence Program of the Ministry of Human Capacities in the frame of Nanotechnology research area of Budapest University of Technology and Economics","award":["BME FIKP-NANO"]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"On the example of the Poynting\u2013Thomson\u2013Zener 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\u2014elastic\u2014level of modeling.<\/jats:p>","DOI":"10.3390\/e22020155","type":"journal-article","created":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T15:51:07Z","timestamp":1580313067000},"page":"155","source":"Crossref","is-referenced-by-count":11,"title":["Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2708-7065","authenticated-orcid":false,"given":"Tam\u00e1s","family":"F\u00fcl\u00f6p","sequence":"first","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5822-6035","authenticated-orcid":false,"given":"R\u00f3bert","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"},{"name":"Department of Theoretical Physics, Wigner Research Centre for Physics, Institute for Particle and Nuclear Physics, 1525 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2492-0392","authenticated-orcid":false,"given":"M\u00e1ty\u00e1s","family":"Sz\u00fccs","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3926-5554","authenticated-orcid":false,"given":"Mohammad","family":"Fawaier","sequence":"additional","affiliation":[{"name":"Department of Building Service and Process Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1016\/j.ijheatmasstransfer.2018.06.067","article-title":"Implicit numerical schemes for generalized heat conduction equations","volume":"126","author":"Rieth","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1515\/jnet-2018-0038","article-title":"Numerical stability with help from entropy: Solving a set of 13 moment equations for shock tube problem","volume":"44","author":"Zinner","year":"2019","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_3","unstructured":"Shang, X., and \u00d6ttinger, H.C. (2018). Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1002\/nme.5532","article-title":"Energy-Entropy-Momentum integration schemes for general discrete non-smooth dissipative problems in thermomechanics","volume":"112","author":"Portillo","year":"2017","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"445206","DOI":"10.1088\/1751-8121\/ab4767","article-title":"Contact variational integrators","volume":"52","author":"Vermeeren","year":"2019","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1088\/1361-6544\/aaa10e","article-title":"Variational discretization of the nonequilibrium thermodynamics of simple systems","volume":"31","author":"Yoshimura","year":"2018","journal-title":"Nonlinearity"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Cou\u00e9raud, B., and Gay-Balmaz, F. (2020). Variational discretization of thermodynamical simple systems on Lie groups. Discret. Cont. Dyn. Syst. Ser. S, 13.","DOI":"10.3934\/dcdss.2020064"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1016\/j.cma.2010.02.014","article-title":"Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part I: Monolithic integrators and their application to finite strain thermoelasticity","volume":"199","author":"Romero","year":"2010","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.1016\/j.cma.2010.03.016","article-title":"Algorithms for coupled problems that preserve symmetries and the laws of thermodynamics: Part II: fractional step methods","volume":"199","author":"Romero","year":"2010","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Berezovski, A., and V\u00e1n, P. (2017). Internal Variables in Thermoelasticity, Springer.","DOI":"10.1007\/978-3-319-56934-5"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/s00707-019-2372-y","article-title":"Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor","volume":"230","author":"Tierra","year":"2019","journal-title":"Acta Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"591","DOI":"10.3311\/PPci.8628","article-title":"Elastic, thermal expansion, plastic and rheological processes\u2014Theory and experiment","volume":"60","author":"Asszonyi","year":"2016","journal-title":"Period. Polytech. Civ. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"F\u00fcl\u00f6p, T., Kov\u00e1cs, R., Lovas, \u00c1., Rieth, \u00c1., Fodor, T., Sz\u00fccs, M., V\u00e1n, P., and Gr\u00f3f, G. (2018). Emergence of non-Fourier hierarchies. Entropy, 20.","DOI":"10.3390\/e20110832"},{"key":"ref_14","unstructured":"Lin, W., Kuwahara, Y., Satoh, T., Shigematsu, N., Kitagawa, Y., Kiguchi, T., and Koizumi, N. (2009, January 28\u201329). A case study of 3D stress orientation determination in Shikoku Island and Kii Peninsula, Japan. Proceedings of the Eurock\u201909, Rock Engineering in Difficult Ground Conditions (Soft Rock and Karst), Cavtat, Croatia."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1019","DOI":"10.1016\/0148-9062(93)90064-K","article-title":"Three-dimensional in situ stress determination by anelastic strain recovery of a rock core","volume":"30","author":"Matsuki","year":"1993","journal-title":"Int. J. Rock Mech. Min Sci. Geomech. Abstr."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1016\/j.ijrmms.2007.10.005","article-title":"Anelastic strain recovery compliance of rocks and its application to in situ stress measurement","volume":"45","author":"Matsuki","year":"2008","journal-title":"Int. J. Rock Mech. Min Sci."},{"key":"ref_17","unstructured":"F\u00fcl\u00f6p, T., and Sz\u00fccs, M. (2018). Analytical solution method for rheological problems of solids. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1002\/mma.2558","article-title":"Kinematic quantities of finite elastic and plastic deformation","volume":"35","year":"2012","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_19","unstructured":"F\u00fcl\u00f6p, T. (2015). Objective thermomechanics. arXiv."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"971","DOI":"10.1007\/s00161-014-0392-3","article-title":"Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory","volume":"27","author":"Asszonyi","year":"2015","journal-title":"Contin. Mech. Thermodyn."},{"key":"ref_21","unstructured":"Davarpanah, S.M., V\u00e1n, P., and V\u00e1s\u00e1rhelyi, B. (2019, January 16\u201318). Investigation of relationship between dynamic and static deformation moduli of rocks. Proceedings of the GEOMATES 2019 International Congress on Geomathematics in Earth-Environmental Sciences, P\u00e9cs, Hungary."},{"key":"ref_22","unstructured":"Hairer, E., Lubich, C., and Wanner, G. (2006). Geometric Numerical Integration, Springer. [2nd ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"237","DOI":"10.3402\/tellusa.v2i4.8607","article-title":"Numerical integration of the barotropic vorticity equation","volume":"2","author":"Charney","year":"1950","journal-title":"Tellus"},{"key":"ref_24","unstructured":"Elaydi, S. (2005). An Introduction to Difference Equations, Springer. [3rd ed.]."},{"key":"ref_25","unstructured":"Matolcsi, T. (2017). Ordinary Thermodynamics \u2013 Nonequilibrium Homogeneous Processes, Society for the Unity of Science and Technology. Available online: http:\/\/energia.bme.hu\/~fulop\/Matolcsi_Ordinary_Thermodynamics_2017-04-26.pdf."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.jcp.2017.01.056","article-title":"Von Neumann stability analysis of globally divergence-free RKDG schemes for the induction equation using multidimensional Riemann solvers","volume":"336","author":"Balsara","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_27","unstructured":"Jury, E.I. (1974). Inners and Stability of Dynamical Systems, John Wiley & Sons."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"J\u00f3zsa, V., and Kov\u00e1cs, R. (2020). Solving Problems in Thermal Engineering \u2013 A Toolbox for Engineers, Springer.","DOI":"10.1007\/978-3-030-33475-8"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/155\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T01:43:08Z","timestamp":1736214188000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,28]]},"references-count":28,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020155"],"URL":"https:\/\/doi.org\/10.3390\/e22020155","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,1,28]]}}}