• 文献检索
  • 文档翻译
  • 深度研究
  • 学术资讯
  • Suppr Zotero 插件Zotero 插件
  • 邀请有礼
  • 套餐&价格
  • 历史记录
应用&插件
Suppr Zotero 插件Zotero 插件浏览器插件Mac 客户端Windows 客户端微信小程序
定价
高级版会员购买积分包购买API积分包
服务
文献检索文档翻译深度研究API 文档MCP 服务
关于我们
关于 Suppr公司介绍联系我们用户协议隐私条款
关注我们

Suppr 超能文献

核心技术专利：CN118964589B侵权必究
粤ICP备2023148730 号-1Suppr @ 2026

文献检索

告别复杂PubMed语法，用中文像聊天一样搜索，搜遍4000万医学文献。AI智能推荐，让科研检索更轻松。

立即免费搜索

文件翻译

保留排版，准确专业，支持PDF/Word/PPT等文件格式，支持 12+语言互译。

免费翻译文档

深度研究

AI帮你快速写综述，25分钟生成高质量综述，智能提取关键信息，辅助科研写作。

立即免费体验

曲面上不可压缩流的无散切向有限元方法

Divergence-free tangential finite element methods for incompressible flows on surfaces.

作者信息

Lederer Philip L, Lehrenfeld Christoph, Schöberl Joachim

机构信息

Institute for Analysis and Scientific Computing TU Wien Vienna Austria.

Institute for Numerical and Applied Mathematics University of Göttingen Göttingen Germany.

出版信息

Int J Numer Methods Eng. 2020 Jun 15;121(11):2503-2533. doi: 10.1002/nme.6317. Epub 2020 Feb 18.

DOI:10.1002/nme.6317
PMID:34853485
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8611805/
Abstract

In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the approximation of a velocity field that lies only in the tangential space of the given geometry. Abandoning -conformity allows us to construct finite elements which are-due to an application of the Piola transformation-exactly tangential. To reintroduce continuity (in a weak sense) we make use of (hybrid) discontinuous Galerkin techniques. To further improve this approach, -conforming finite elements can be used to obtain exactly divergence-free velocity solutions. We present several new finite element discretizations. On a number of numerical examples we examine and compare their qualitative properties and accuracy.

摘要

在这项工作中，我们考虑二维流形上不可压缩流的数值解。虽然速度和压力空间的相容性要求在平面情形中是已知的，但还必须处理仅位于给定几何形状切空间中的速度场的逼近问题。放弃(\mathbb{P})-协调性使我们能够构造有限元，由于应用了皮奥拉变换，这些有限元恰好是切向的。为了重新引入（弱意义下的）连续性，我们使用（混合）间断伽辽金技术。为了进一步改进这种方法，可以使用(\mathbb{P})-协调有限元来获得完全无散度的速度解。我们给出了几种新的有限元离散化方法。在一些数值例子中，我们检验并比较了它们的定性性质和精度。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/0885fded8082/NME-121-2503-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/d9757d9be1ee/NME-121-2503-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/32f1c31fc468/NME-121-2503-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/eccfb1a2ec13/NME-121-2503-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3dddcf5bb9e4/NME-121-2503-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/bfc7c15cdf43/NME-121-2503-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/385dedc4e940/NME-121-2503-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/2d9e75fec9ef/NME-121-2503-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/a86c52424980/NME-121-2503-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/5b1278a060b8/NME-121-2503-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/25bbe1239567/NME-121-2503-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3f82ab1e9763/NME-121-2503-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3ea8dc5bf2cd/NME-121-2503-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/44022fc181fe/NME-121-2503-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/c568dbb92294/NME-121-2503-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/1d703857b9bb/NME-121-2503-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/0885fded8082/NME-121-2503-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/d9757d9be1ee/NME-121-2503-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/32f1c31fc468/NME-121-2503-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/eccfb1a2ec13/NME-121-2503-g016.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3dddcf5bb9e4/NME-121-2503-g015.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/bfc7c15cdf43/NME-121-2503-g014.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/385dedc4e940/NME-121-2503-g013.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/2d9e75fec9ef/NME-121-2503-g012.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/a86c52424980/NME-121-2503-g011.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/5b1278a060b8/NME-121-2503-g010.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/25bbe1239567/NME-121-2503-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3f82ab1e9763/NME-121-2503-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/3ea8dc5bf2cd/NME-121-2503-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/44022fc181fe/NME-121-2503-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/c568dbb92294/NME-121-2503-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/1d703857b9bb/NME-121-2503-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fbc0/8611805/0885fded8082/NME-121-2503-g003.jpg

相似文献

1
Divergence-free tangential finite element methods for incompressible flows on surfaces.曲面上不可压缩流的无散切向有限元方法
Int J Numer Methods Eng. 2020 Jun 15;121(11):2503-2533. doi: 10.1002/nme.6317. Epub 2020 Feb 18.
2
Divergence-Conforming Velocity and Vorticity Approximations for Incompressible Fluids Obtained with Minimal Facet Coupling.通过最小面元耦合获得的不可压缩流体的散度一致速度和涡度近似
J Sci Comput. 2023;95(3):91. doi: 10.1007/s10915-023-02203-8. Epub 2023 May 11.
3
An H(div)-conforming Finite Element Method for Biot's Consolidation Model.一种用于比奥固结模型的H(div)协调有限元方法。
East Asian J Applied Math. 2019 Aug;9(3):558-579. doi: 10.4208/eajam.170918.261218.
4
Gradient-Robust Hybrid DG Discretizations for the Compressible Stokes Equations.可压缩斯托克斯方程的梯度鲁棒混合间断伽辽金离散化
J Sci Comput. 2024;100(2):54. doi: 10.1007/s10915-024-02605-2. Epub 2024 Jul 4.
5
New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows.基于隐式界面方法（IIM）的不可压缩流中不可拉伸界面的新型有限差分方法。
East Asian J Applied Math. 2011 Jan 1;1(2):155-171. doi: 10.4208/eajam.030510.250910a.
6
Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods.用标准速度校正投影法求解不可压缩曲面斯托克斯方程
Entropy (Basel). 2022 Sep 23;24(10):1338. doi: 10.3390/e24101338.
7
Finite Element Iterative Methods for the 3D Steady Navier--Stokes Equations.三维稳态纳维-斯托克斯方程的有限元迭代方法
Entropy (Basel). 2021 Dec 9;23(12):1659. doi: 10.3390/e23121659.
8
The meshless local Petrov-Galerkin method based on moving Kriging interpolation for solving the time fractional Navier-Stokes equations.基于移动克里金插值的无网格局部彼得罗夫-伽辽金方法求解时间分数阶纳维-斯托克斯方程
Springerplus. 2016 Apr 6;5:417. doi: 10.1186/s40064-016-2047-2. eCollection 2016.
9
A divergence-free semi-implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics.一种用于理想、粘性和电阻磁流体动力学的无散半隐式有限体积格式。
Int J Numer Methods Fluids. 2019 Jan 10;89(1-2):16-42. doi: 10.1002/fld.4681. Epub 2018 Sep 25.
10
Assessment of 4D flow MRI's quality by verifying its Navier-Stokes compatibility.评估 4D 流 MRI 的纳维斯托克斯兼容性以保证其质量。
Int J Numer Method Biomed Eng. 2022 Jun;38(6):e3603. doi: 10.1002/cnm.3603. Epub 2022 May 9.

引用本文的文献

1
Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods.用标准速度校正投影法求解不可压缩曲面斯托克斯方程
Entropy (Basel). 2022 Sep 23;24(10):1338. doi: 10.3390/e24101338.

本文引用的文献

1
Hydrodynamic theory for nematic shells: The interplay among curvature, flow, and alignment.向列型壳层的流体动力学理论：曲率、流动与取向之间的相互作用
Phys Rev E. 2016 Aug;94(2-1):020701. doi: 10.1103/PhysRevE.94.020701. Epub 2016 Aug 8.