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多面体网格上三维不可压缩流动的罚虚拟单元法

Penalty Virtual Element Method for the 3D Incompressible Flow on Polyhedron Mesh.

作者信息

Li Lulu, Su Haiyan, He Yinnian

机构信息

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China.

出版信息

Entropy (Basel). 2022 Aug 15;24(8):1129. doi: 10.3390/e24081129.

DOI:10.3390/e24081129
PMID:36010792
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9407093/
Abstract

In this paper, a penalty virtual element method (VEM) on polyhedral mesh for solving the 3D incompressible flow is proposed and analyzed. The remarkable feature of VEM is that it does not require an explicit computation of the trial and test space, thereby bypassing the obstacle of standard finite element discretizations on arbitrary mesh. The velocity and pressure are approximated by the practical significative lowest equal-order virtual element space pair (Xh,Qh) which does not satisfy the discrete inf-sup condition. Combined with the penalty method, the error estimation is proved rigorously. Numerical results on the 3D polygonal mesh illustrate the theoretical results and effectiveness of the proposed method.

摘要

本文提出并分析了一种用于求解三维不可压缩流的多面体网格罚虚拟单元法（VEM）。VEM的显著特点是不需要显式计算试验空间和测试空间，从而绕过了任意网格上标准有限元离散化的障碍。速度和压力由不满足离散下-上条件的具有实际意义的最低等阶虚拟单元空间对（Xh,Qh）近似。结合罚函数法，严格证明了误差估计。三维多边形网格上的数值结果验证了所提方法的理论结果和有效性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/48d8ee0d9cf5/entropy-24-01129-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/147a46744f4c/entropy-24-01129-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/166c8cf15034/entropy-24-01129-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/0fd902cce804/entropy-24-01129-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/de0a916485ca/entropy-24-01129-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/851b27721160/entropy-24-01129-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/445865b3579d/entropy-24-01129-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/0e33002c73d0/entropy-24-01129-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/48d8ee0d9cf5/entropy-24-01129-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/147a46744f4c/entropy-24-01129-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/166c8cf15034/entropy-24-01129-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/0fd902cce804/entropy-24-01129-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/de0a916485ca/entropy-24-01129-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/851b27721160/entropy-24-01129-g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/445865b3579d/entropy-24-01129-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/0e33002c73d0/entropy-24-01129-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/cc4d/9407093/48d8ee0d9cf5/entropy-24-01129-g008.jpg

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