Parallel domain decomposition method for finite element approximation of 3D steady state non-Newtonian fluids

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題名:	Parallel domain decomposition method for finite element approximation of 3D steady state non-Newtonian fluids
作者:	黃楓南;Shiu, Wen-Shin;Hwang, Feng-Nan;Cai, Xiao-Chuan
貢獻者:	理學院數學系
關鍵詞:	Algorithms;Computational fluid dynamics;Cylinders;Decomposition;Finite element method;Fluid flow;Mathematical analysis;Mathematical models;Navier-Stokes equations;Newton-Krylov-Schwarz algorithm;non-Newtonian fluids;parallel computing;stabilized finite element method;Three dimensional
日期:	2015-07-20
上傳時間:	2026-04-23 16:20:04 (UTC+8)
出版者:	John Wiley and Sons Ltd;Bognor Regis: Blackwell Publishing Ltd
摘要:	摘要： SummaryWe introduce a stabilized finite element method for the 3D non‐Newtonian Navier–Stokes equations and a parallel domain decomposition method for solving the sparse system of nonlinear equations arising from the discretization. Non‐Newtonian flow problems are, generally speaking, more challenging than Newtonian flows because the nonlinearities are not only in the convection term but also in the viscosity term, which depends on the shear rate. Many good iterative methods and preconditioning techniques that work well for the Newtonian flows do not work well for the non‐Newtonian flows. We employ a Galerkin/least squares finite element method, with stabilization parameters adjusted to count the non‐Newtonian effect, to discretize the equations, and the resulting highly nonlinear system of equations is solved by a Newton–Krylov–Schwarz algorithm. In this study, we apply the proposed method to some inelastic power‐law fluid flows through the eccentric annuli with inner cylinder rotation and investigate the robustness of the method with respect to some physical parameters, including the power‐law index and the Reynolds number ratios. We then report the superlinear speedup achieved by the domain decomposition algorithm on a computer with up to 512 processors. Copyright © 2015 John Wiley & Sons, Ltd. We introduce a stabilized finite element method for 3D non‐Newtonian fluids and a parallel algorithm for solving the large nonlinear system of algebraic equations. The domain decomposition‐based preconditioning algorithm is quite effective for these highly ill‐conditioned problems with a wide range of physical parameters. Using numerical experiments, we provide some quantitative analysis of certain rotational eccentric annular flows in terms of pressure (left) and shear stress distributions (right) for the pseudoplastic case (top) and the dilatant case (bottom). 其他題名： Int. J. Numer. Meth. Fluids 出版者： Bognor Regis: Blackwell Publishing Ltd 出版日期： 2015-07-20 出處： International journal for numerical methods in fluids, 2015-07, Vol.78 (8), p.502-520 資源來源： Wiley Online Library Journals 版權： Copyright © 2015 John Wiley & Sons, Ltd. 識別號： ISSN: 0271-2091 識別號： ISSN: 1097-0363 識別號： EISSN: 1097-0363 識別號： DOI: 10.1002/fld.4027 識別號： CODEN: IJNFDW
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