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Finally, a numerical scheme is derived and proved to coincide with an approximation designed in [&lt;xref ref-type=\"bibr\" rid=\"b3\"&gt;3&lt;\/xref&gt;] and extended to second order and two space dimensions in [&lt;xref ref-type=\"bibr\" rid=\"b6\"&gt;6&lt;\/xref&gt;]. Some numerical tests are presented.&lt;\/p&gt;<\/jats:p>","DOI":"10.3934\/nhm.2022018","type":"journal-article","created":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T10:17:07Z","timestamp":1648894627000},"page":"593","source":"Crossref","is-referenced-by-count":1,"title":["Modelling and numerical study of the polyatomic bitemperature Euler system"],"prefix":"10.3934","volume":"17","author":[{"given":"Denise","family":"Aregba-Driollet","sequence":"first","affiliation":[{"name":"Univ. Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"St\u00e9phane","family":"Brull","sequence":"additional","affiliation":[{"name":"Univ. 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