{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T18:43:58Z","timestamp":1781808238901,"version":"3.54.5"},"reference-count":45,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51806116"],"award-info":[{"award-number":["51806116"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2019M662521"],"award-info":[{"award-number":["2019M662521"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A shock wave that is characterized by sharp physical gradients always draws the medium out of equilibrium. In this work, both hydrodynamic and thermodynamic nonequilibrium effects around the shock wave are investigated using a discrete Boltzmann model. Via Chapman\u2013Enskog analysis, the local equilibrium and nonequilibrium velocity distribution functions in one-, two-, and three-dimensional velocity space are recovered across the shock wave. Besides, the absolute and relative deviation degrees are defined in order to describe the departure of the fluid system from the equilibrium state. The local and global nonequilibrium effects, nonorganized energy, and nonorganized energy flux are also investigated. Moreover, the impacts of the relaxation frequency, Mach number, thermal conductivity, viscosity, and the specific heat ratio on the nonequilibrium behaviours around shock waves are studied. This work is helpful for a deeper understanding of the fine structures of shock wave and nonequilibrium statistical mechanics.<\/jats:p>","DOI":"10.3390\/e22121397","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T08:59:34Z","timestamp":1607590774000},"page":"1397","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Hydrodynamic and Thermodynamic Nonequilibrium Effects around Shock Waves: Based on a Discrete Boltzmann Method"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4116-1321","authenticated-orcid":false,"given":"Chuandong","family":"Lin","sequence":"first","affiliation":[{"name":"Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China"},{"name":"Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7052-8375","authenticated-orcid":false,"given":"Xianli","family":"Su","sequence":"additional","affiliation":[{"name":"Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yudong","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mechanics and Safety Engineering, Zhengzhou University, Zhengzhou 450001, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zohuri, B., and Fathi, N. 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