适用于微粒流和Stokes方程的最佳收敛且易于实现的浸入边界方法

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2023-05-01 DOI:10.1051/m2an/2023010

Michel Duprez, Vanessa Lleras, Alexei Lozinski

{"title":"适用于微粒流和Stokes方程的最佳收敛且易于实现的浸入边界方法","authors":"Michel Duprez, Vanessa Lleras, Alexei Lozinski","doi":"10.1051/m2an/2023010","DOIUrl":null,"url":null,"abstract":"We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ -FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H 1 norm for the velocity and L 2 for pressure; numerically also in the L 2 norm for the velocity).","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":"52 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"<i>ϕ</i>-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations\",\"authors\":\"Michel Duprez, Vanessa Lleras, Alexei Lozinski\",\"doi\":\"10.1051/m2an/2023010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ -FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H 1 norm for the velocity and L 2 for pressure; numerically also in the L 2 norm for the velocity).\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":\"52 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1051/m2an/2023010\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/m2an/2023010","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 1

摘要

我们提出了一种浸入式边界方法来模拟由Stokes方程离散化的流体中刚性粒子的蠕动运动，这要归功于未拟合网格上的有限元策略，称为φ -FEM，该策略使用具有水平集函数的固体描述。我们的方法的优点之一是使用了标准的有限元空间和经典的积分工具，同时保持了最优的收敛性(理论上在速度的h1范数和压力的l2范数;数值上也在速度的l2范数中)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

ϕ-FEM: an optimally convergent and easily implementable immersed boundary method for particulate flows and Stokes equations

We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called ϕ -FEM, that uses the description of the solid with a level-set function. One of the advantages of our method is the use of standard finite element spaces and classical integration tools, while maintaining the optimal convergence (theoretically in the H 1 norm for the velocity and L 2 for pressure; numerically also in the L 2 norm for the velocity).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.