An explicit Chebyshev pseudospectral multigrid method for incompressible Navier–Stokes equations

The two-dimensional steady incompressible Navier–Stokes equations in the form of primitive variables have been solved by Chebyshev pseudospectral method. The pressure and velocities are coupled by artificial compressibility method and the NS equations are solved by pseudotime method with an explicit...

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Vydáno v:Computers & fluids Ročník 39; číslo 1; s. 178 - 188
Hlavní autoři: Zhang, W., Zhang, C.H., Xi, G.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 2010
Elsevier
Témata:
Burgers equation
Computational fluid dynamics
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fluid flow
Fundamental areas of phenomenology (including applications)
Grid method
Mathematical analysis
Mathematical models
Multigrid methods
Navier-Stokes equations
Physics
Taylor vortex
Computational fluid dynamics
Digital simulation
Burgers equation
Cavity flow
Moving wall
Algorithms
Laminar flow
Multigrid
Modelling
Incompressible fluid
Runge-Kutta methods
Iterative methods
Numerical convergence
Navier-Stokes equations
ISSN:0045-7930, 1879-0747
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Shrnutí:The two-dimensional steady incompressible Navier–Stokes equations in the form of primitive variables have been solved by Chebyshev pseudospectral method. The pressure and velocities are coupled by artificial compressibility method and the NS equations are solved by pseudotime method with an explicit four-step Runge–Kutta integrator. In order to reduce the computational time cost, we propose the spectral multigrid algorithm in full approximation storage (FAS) scheme and implement it through V-cycle multigrid and full multigrid (FMG) strategies. Four iterative methods are designed including the single grid method; the full single grid method; the V-cycle multigrid method and the FMG method. The accuracy and efficiency of the numerical methods are validated by three test problems: the modified one-dimensional Burgers equation; the Taylor vortices and the two-dimensional lid driven cavity flow. The computational results fit well with the exact or benchmark solutions. The spectral accuracy can be maintained by the single grid method as well as the multigrid ones, while the time cost is greatly reduced by the latter. For the lid driven cavity flow problem, the FMG is proved to be the most efficient one among the four iterative methods. A speedup of nearly two orders of magnitude can be achieved by the three-level multigrid method and at least one order of magnitude by the two-level multigrid method.
Bibliografie:ObjectType-Article-1
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ISSN:0045-7930
1879-0747
DOI:10.1016/j.compfluid.2009.08.001