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A stable and scalable hybrid solver for rate-type non-Newtonian fluid models
Lee, Young-Ju1; Leng, Wei2,3; Zhang, Chen-Song2,3
2016-07-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume300Pages:103-118
AbstractWe present and analyze hybrid discretization schemes for rate-type non-Newtonian fluids models. The method employs higher order conforming approximations for velocity and pressure of the Stokes equation and lower order approximations such as piecewise linear or piecewise constant for conformation tensor. To reduce the accuracy gap, the constitutive equation is discretized on a refined mesh, which is obtained by subdividing the mesh for the velocity and pressure. The temporal discretization is made by the standard semi-Lagrangian scheme. The fully discrete nonlinear system is shown to be solved iteratively by applying the three steps:(1) locating the characteristic feet of fluid particles, (2) solving the constitutive equation, and (3) solving the momentum and continuity equations (Stokes type equation). To achieve a scalability of the solution process, we employ an auxiliary space preconditioning method for the solution to the conforming finite element methods for the Stokes equation. This method is basically two-grid method, in which lower-order finite element spaces are employed as auxiliary spaces. It is shown to not only lead to the mesh independent convergence, but also improve robustness and scalability. Stability analysis shows that if Delta t = O(h(d)), where d is the dimension of domain, then the scheme admits a globally unique solution. A number of full 3D test cases are provided to demonstrate the advantages of the proposed numerical techniques in relation to efficiency, robustness, and weak scalability. (C) 2015 Elsevier B.V. All rights reserved.
KeywordFinite element methods Scalable solver Stable discretization Non-Newtonian models
DOI10.1016/j.cam.2015.12.026
Language英语
Funding ProjectNSF-DMS[0915028] ; NSF-DMS[1358953] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000371551300009
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22242
Collection计算数学与科学工程计算研究所
Affiliation1.Texas State Univ, Dept Math, San Marcos, TX 78666 USA
2.Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China
3.Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Lee, Young-Ju,Leng, Wei,Zhang, Chen-Song. A stable and scalable hybrid solver for rate-type non-Newtonian fluid models[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2016,300:103-118.
APA Lee, Young-Ju,Leng, Wei,&Zhang, Chen-Song.(2016).A stable and scalable hybrid solver for rate-type non-Newtonian fluid models.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,300,103-118.
MLA Lee, Young-Ju,et al."A stable and scalable hybrid solver for rate-type non-Newtonian fluid models".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 300(2016):103-118.
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