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

Shiu, Wen‐Shin; Hwang, Feng‐Nan; Cai, Xiao‐Chuan

doi:10.1002/fld.4027

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

Journal Article · Wed Apr 15 00:00:00 EDT 2015 · International Journal for Numerical Methods in Fluids

DOI:https://doi.org/10.1002/fld.4027· OSTI ID:1400708

Shiu, Wen‐Shin ^[1]; Hwang, Feng‐Nan ^[2]; Cai, Xiao‐Chuan ^[3]

Department of Mathematics National Central University Jhongli District, Taoyuan City 32001 Taiwan, Shenzhen Institutes of Advanced Technology Chinese Academy of Sciences Shenzhen, Guangdong 518055 China
Department of Mathematics National Central University Jhongli District, Taoyuan City 32001 Taiwan
Department of Computer Science University of Colorado Boulder CO 80309 USA

Summary

We 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.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

OSTI ID:: 1400708

Journal Information:: International Journal for Numerical Methods in Fluids, Journal Name: International Journal for Numerical Methods in Fluids Journal Issue: 8 Vol. 78; ISSN 0271-2091

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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