{"title":"Explicit exact solutions for plane shock waves in dilute polyatomic gases","authors":"F. J. Uribe, R. M. Velasco, W. Marques Jr.","doi":"10.1111/sapm.12776","DOIUrl":null,"url":null,"abstract":"<p>The exact solutions for the Navier–Stokes–Fourier equations in the case of plane shock waves for dilute monatomic gases with constant transport coefficients were found by Becker in 1922. The solutions obtained are limited for a Prandtl's number given by <span></span><math>\n <semantics>\n <mrow>\n <mi>P</mi>\n <mi>r</mi>\n <mo>=</mo>\n <mn>3</mn>\n <mo>/</mo>\n <mn>4</mn>\n </mrow>\n <annotation>$Pr=3/4$</annotation>\n </semantics></math>. Besides the solutions for the speed and temperature, profiles were given in an implicit way. In this paper, we consider Becker's model to find some exact <i>explicit</i> solutions for dilute polyatomic gases.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2024-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12776","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The exact solutions for the Navier–Stokes–Fourier equations in the case of plane shock waves for dilute monatomic gases with constant transport coefficients were found by Becker in 1922. The solutions obtained are limited for a Prandtl's number given by . Besides the solutions for the speed and temperature, profiles were given in an implicit way. In this paper, we consider Becker's model to find some exact explicit solutions for dilute polyatomic gases.
贝克尔于 1922 年发现了纳维-斯托克斯-傅里叶方程在具有恒定传输系数的稀释单原子气体平面冲击波情况下的精确解。所得到的解仅限于普朗特数为 P r = 3 / 4 $Pr=3/4$的情况。除了速度和温度的解之外，曲线也是以隐式方式给出的。在本文中，我们将考虑贝克尔模型，为稀释多原子气体找到一些精确的显式解。
期刊介绍：
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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