A new parallel finite element algorithm for the stationary Navier-Stokes equations

Authors:
Yueqiang Shang;Yinnian He;Do Wan Kim;Xiaojun Zhou
Affiliations:
Department of Mathematics, Inha University, Incheon, 402-751, Republic of Korea and School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, PR China;Faculty of Science, Xi'an Jiaotong University, Xi'an, 710049, PR China;Department of Mathematics, Inha University, Incheon, 402-751, Republic of Korea;School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, PR China
Venue:
Finite Elements in Analysis and Design
Year:
2011

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Abstract

Based on two-grid discretization, a new parallel finite element algorithm for the stationary Navier-Stokes equations is proposed and analyzed. This algorithm first solves the Navier-Stokes equations using a coarse grid, and then corrects the resultant residual on a fine grid by solving local Navier-Stokes equations in a parallel manner with homogeneous boundary conditions. Existing sequential Navier-Stokes solver is available for each problem on sub-domains, so that the proposed parallel algorithm can be implemented on the top of existing sequential software. The error bounds of the approximate solution are estimated. Moreover, the efficiency of the algorithm is also demonstrated by numerical simulations of the lid-driven cavity flow, the backward-facing step flow, and the flow past a circular cylinder.