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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 Publication JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS ISSN 0377-0427 Volume 300Pages:103-118 Abstract We 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. Keyword Finite element methods Scalable solver Stable discretization Non-Newtonian models DOI 10.1016/j.cam.2015.12.026 Language 英语 Funding Project NSF-DMS[0915028] ; NSF-DMS[1358953] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323] WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000371551300009 Publisher ELSEVIER SCIENCE BV Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/22242 Collection 计算数学与科学工程计算研究所 Corresponding Author Lee, Young-Ju Affiliation 1.Texas State Univ, Dept Math, San Marcos, TX 78666 USA2.Acad Math & Syst Sci, NCMIS, Beijing 100190, Peoples R China3.Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China Recommended CitationGB/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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