{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:32:35Z","timestamp":1760146355000,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T00:00:00Z","timestamp":1729814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, we mainly studied the Riemann problem and wave interaction of a simplified magnetohydrodynamic equation system. Due to the complex Riemann problem and wave interactions in the magnetohydrodynamic equations, most previous studies either did not investigate the interaction of elementary waves or, if they did, lacked supporting numerical experiments. This paper simplifies the magnetohydrodynamic equations using variable substitution. Using the characteristic line method to solve the Riemann problem and elementary wave interaction of the simplified magnetohydrodynamic equations, the form of the solution is more symmetrical and the interaction between waves has also become more regular. The correctness of the results was verified by numerical experiments.<\/jats:p>","DOI":"10.3390\/sym16111425","type":"journal-article","created":{"date-parts":[[2024,10,25]],"date-time":"2024-10-25T08:42:13Z","timestamp":1729845733000},"page":"1425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Riemann Problem and Elementary Wave Interactions for a Simplified Magnetic Fluid Model"],"prefix":"10.3390","volume":"16","author":[{"given":"Kangning","family":"Yu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Changji University, Changji 831100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuo","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Changji University, Changji 831100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1275-2982","authenticated-orcid":false,"given":"Guodong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,25]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Theory of the laminar flow of an electrically conductive liquid in a homogeneous magnetic field","volume":"6","author":"Hartmann","year":"1937","journal-title":"J. Math.-Fys. Meddelelser"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1002\/asna.2103010302","article-title":"Mean-field approach to spherical dynamo models","volume":"301","author":"Radler","year":"1980","journal-title":"J. Astronom. Nachr."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"755","DOI":"10.3934\/cpaa.2013.12.755","article-title":"The Riemann problem of conservation laws in magnetogasdynamics","volume":"12","author":"Hu","year":"2013","journal-title":"J. Commun. Pure Appl. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1016\/j.jmaa.2012.07.064","article-title":"Riemann problem and wave interactions in magnetogasdynamics","volume":"397","author":"Liu","year":"2013","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.1007\/s11012-014-0009-8","article-title":"Riemann solution for ideal isentropic magnetogasdynamics","volume":"49","author":"Kuila","year":"2014","journal-title":"J. Mecc."},{"key":"ref_6","first-page":"119","article-title":"Riemann solution for one dimensional non-ideal isentropic magnetogasdynamics","volume":"35","author":"Kuila","year":"2016","journal-title":"J. Comput. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s13226-016-0172-9","article-title":"Elementary wave interactions in magnetogasdynamics","volume":"47","author":"Liu","year":"2016","journal-title":"J. Indian J. Pure Appl. Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1016\/j.jmaa.2013.12.025","article-title":"Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas","volume":"413","author":"Yang","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3101","DOI":"10.1007\/s40840-022-01362-5","article-title":"Vanishing Magnetic Field Limits of Solutions to the Isentropic Chaplygin Gas Magnetogasdynamics Equations","volume":"45","author":"Zhiqiang","year":"2022","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1134\/S1810232824020012","article-title":"Dynamics of Condensation and Evaporation of Liquid Nitrogen in a Closed Vessel Pressurized with Helium, Nitrogen, and Their Mixture","volume":"33","author":"Trushlyakov","year":"2024","journal-title":"J. Eng. Thermophys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"A2224","DOI":"10.1137\/23M1580863","article-title":"A New Thermodynamically Compatible Finite Volume Scheme for Lagrangian Gas Dynamics","volume":"46","author":"Boscheri","year":"2024","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1425\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:20:39Z","timestamp":1760113239000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1425"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,25]]},"references-count":11,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["sym16111425"],"URL":"https:\/\/doi.org\/10.3390\/sym16111425","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,10,25]]}}}