基于非协调有限元的平稳Navier-Stokes方程空间迭代方法比较研究

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

East Asian Journal on Applied Mathematics Pub Date : 2022-06-01 DOI:10.4208/eajam.300121.261221

Jiawei Gao null, Jian Li

{"title":"基于非协调有限元的平稳Navier-Stokes方程空间迭代方法比较研究","authors":"Jiawei Gao null, Jian Li","doi":"10.4208/eajam.300121.261221","DOIUrl":null,"url":null,"abstract":". Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming ﬁnite element pairs P 1 N C - P 1 , in-cluding simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical ﬁndings. In partic-ular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations\",\"authors\":\"Jiawei Gao null, Jian Li\",\"doi\":\"10.4208/eajam.300121.261221\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming ﬁnite element pairs P 1 N C - P 1 , in-cluding simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical ﬁndings. In partic-ular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.\",\"PeriodicalId\":48932,\"journal\":{\"name\":\"East Asian Journal on Applied Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2022-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"East Asian Journal on Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4208/eajam.300121.261221\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"East Asian Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/eajam.300121.261221","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

．基于最低阶非协调有限元对p1 N C - p1，采用三种不同的空间迭代方法求解稳定Navier-Stokes方程，包括简单迭代法、Oseen迭代法和牛顿迭代法。研究了这些方法的稳定性和收敛性，并讨论了它们的CPU时间和数值收敛速度。数值结果与理论结果吻合较好。数值实验表明，对于大黏度方程，牛顿法收敛速度快，而Oseen法更适合于小黏度方程。

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

Comparative Study of Space Iteration Methods Based on Nonconforming Finite Element for Stationary Navier-Stokes Equations

. Steady Navier-Stokes equations are solved by three different space iteration methods based on the lowest order nonconforming ﬁnite element pairs P 1 N C - P 1 , in-cluding simple, Oseen, and Newton iterative methods. The stability and convergence of these methods are studied, and their CPU time and numerical convergence rate are discussed. Numerical results are in good agreement with theoretical ﬁndings. In partic-ular, numerical experiments show that for large viscosity, the Newton method converges faster than to others, whereas the Oseen method is more suitable for the equations with small viscosity.

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

East Asian Journal on Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.60

自引率

8.30%

发文量

期刊介绍： The East Asian Journal on Applied Mathematics (EAJAM) aims at promoting study and research in Applied Mathematics in East Asia. It is the editorial policy of EAJAM to accept refereed papers in all active areas of Applied Mathematics and related Mathematical Sciences. Novel applications of Mathematics in real situations are especially welcome. Substantial survey papers on topics of exceptional interest will also be published occasionally.