{"title":"Turbulent Kinetic Energy in an Approximate Riemann Solver","authors":"M. I. Boldyrev","doi":"10.1134/s0965542524700532","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Turbulent kinetic energy (TKE) is taken into account in the approximate HLLC Riemann solver. The Euler equations are supplemented with a hyperbolic equation for TKE, and turbulent pressure is taken into account in the momentum and energy balance equations. The Jacobian of this system of equations and its eigenvalues are found, which are used to modify the HLLC solver. The validity of TKE allowance in the modified HLLC Riemann solver is verified by solving Sod’s problem. It is shown that the scheme is unstable at high turbulent pressure if turbulence is ignored in the computation of characteristic velocities.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700532","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Turbulent kinetic energy (TKE) is taken into account in the approximate HLLC Riemann solver. The Euler equations are supplemented with a hyperbolic equation for TKE, and turbulent pressure is taken into account in the momentum and energy balance equations. The Jacobian of this system of equations and its eigenvalues are found, which are used to modify the HLLC solver. The validity of TKE allowance in the modified HLLC Riemann solver is verified by solving Sod’s problem. It is shown that the scheme is unstable at high turbulent pressure if turbulence is ignored in the computation of characteristic velocities.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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