Parallel defect-correction algorithms based on finite element discretization for the Navier–Stokes equations

•Two parallel defect-correction algorithms for the Navier–Stokes equations are presented.•The algorithms are able to simulate high Reynolds numbers flows on relatively coarse grids.•The parallel algorithms are easy to implement based on an existing sequential solver.•The algorithms have low communic...

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Bibliographic Details
Published in:Computers & fluids Vol. 79; pp. 200 - 212
Main Author: Shang, Yueqiang
Format: Journal Article
Language:English
Published: Elsevier Ltd 25.06.2013
Subjects:
Algorithms
Computer simulation
Defect-correction method
Discretization
Domain decomposition
Finite element
Finite element method
Mathematical analysis
Mathematical models
Navier-Stokes equations
Parallel algorithm
Parallel computing
Navier–Stokes equations
Parallel computing
Parallel algorithm
Defect-correction method
Domain decomposition
Finite element
ISSN:0045-7930, 1879-0747
Online Access:Get full text
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Summary:•Two parallel defect-correction algorithms for the Navier–Stokes equations are presented.•The algorithms are able to simulate high Reynolds numbers flows on relatively coarse grids.•The parallel algorithms are easy to implement based on an existing sequential solver.•The algorithms have low communication cost.•Numerical results demonstrated the efficiency of the algorithms. Based on a fully overlapping domain decomposition technique and finite element discretization, two parallel defect-correction algorithms for the stationary Navier–Stokes equations with high Reynolds numbers are proposed and investigated. In these algorithms, each processor first solves an artificial viscosity stabilized Navier–Stokes equations by Newton or Picard iterative method, and then diffuses the system in the correction steps where only a linear problem needs to be solved at each step. All the computations are performed in parallel on global composite meshes that are fine around a particular subdomain and coarse elsewhere. The algorithms have low communication complexity. They can yield an approximate solution with an accuracy comparable to that of the standard finite element solution. Numerical tests demonstrated the effectiveness of the algorithms.
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ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2013.03.021