A stable and scalable hybrid solver for rate-type non-Newtonian fluid models

doi:10.1016/j.cam.2015.12.026

	A stable and scalable hybrid solver for rate-type non-Newtonian fluid models
	Lee, Young-Ju 1; Leng, Wei2,3 ; Zhang, Chen-Song2,3
	2016-07-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	300 页码:103-118
摘要	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.
关键词	Finite element methods Scalable solver Stable discretization Non-Newtonian models
DOI	10.1016/j.cam.2015.12.026
语种	英语
资助项目	NSF-DMS[0915028] ; NSF-DMS[1358953] ; National Natural Science Foundation of China[91430215] ; National Natural Science Foundation of China[91530323]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000371551300009
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22242
专题	计算数学与科学工程计算研究所
通讯作者	Lee, Young-Ju
作者单位	1.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
推荐引用方式 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.