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A Simplified Parallel Two-Level Iterative Method for Simulation of Incompressible Navier-Stokes Equations

Published online by Cambridge University Press:  09 September 2015

Yueqiang Shang  and
Jin Qin
Yueqiang Shang*
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
Jin Qin
Affiliation:
School of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, China
*
*Corresponding author. Email: [email protected] (Y. Q. Shang), [email protected] (J. Qin)
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Abstract

Based on two-grid discretization, a simplified parallel iterative finite element method for the simulation of incompressible Navier-Stokes equations is developed and analyzed. The method is based on a fixed point iteration for the equations on a coarse grid, where a Stokes problem is solved at each iteration. Then, on overlapped local fine grids, corrections are calculated in parallel by solving an Oseen problem in which the fixed convection is given by the coarse grid solution. Error bounds of the approximate solution are derived. Numerical results on examples of known analytical solutions, lid-driven cavity flow and backward-facing step flow are also given to demonstrate the effectiveness of the method.

Keywords

65N5576D0776M10Navier-Stokes equationsfinite elementtwo-level methodparallel algorithm
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 6 , December 2015 , pp. 715 - 735
Copyright
Copyright © Global-Science Press 2015 

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