{"title":"A rotational velocity-correction projection method for the Micropolar Navier-Stokes equations","authors":"","doi":"10.1016/j.apnum.2024.07.013","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we introduce a velocity correction projection method for the Micropolar Navier-Stokes Equations. The velocity correction method are adopted to approximate the time derivative term, stability analysis and error estimation of the first-order semi-discrete scheme are proved. At the same time, the optimal error estimate using the technique of dual norm are obtained. In this way, the divergence free of the velocity <strong>u</strong> can be conserved. Finally, the numerical results show the method has an optimal convergence order. The numerical results are consistent with our theoretical analysis, and our method is effective.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927424001934","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
In this paper, we introduce a velocity correction projection method for the Micropolar Navier-Stokes Equations. The velocity correction method are adopted to approximate the time derivative term, stability analysis and error estimation of the first-order semi-discrete scheme are proved. At the same time, the optimal error estimate using the technique of dual norm are obtained. In this way, the divergence free of the velocity u can be conserved. Finally, the numerical results show the method has an optimal convergence order. The numerical results are consistent with our theoretical analysis, and our method is effective.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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