Implicit eighth-order central compact scheme for the numerical simulation of steady and unsteady incompressible Navier-Stokes equations

The pseudo-compressibility method, with an implicit eighth-order central compact scheme, is proposed to solve the steady and unsteady incompressible Navier-Stokes equations. In this method, the spatial discretisation comprises an eighth-order compact scheme with stable boundary closures and a tenth-...

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Bibliographic Details
Published in:International journal of computational fluid dynamics 2012-04, Vol.26 (4), p.247-261
Main Authors: Zhang, JinBai, Qian, ZhanSen
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
compact scheme
Computational fluid dynamics
Computer simulation
Fluid dynamics
Fluid flow
implicit high-order scheme
Incompressible flow
incompressible Navier-Stokes equations
Lower-Upper Symmetric Gauss-Seidel scheme
Mathematical analysis
Mathematical models
Navier-Stokes equations
Quantum theory
Simulation
Unsteady
unsteady flow
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Summary:The pseudo-compressibility method, with an implicit eighth-order central compact scheme, is proposed to solve the steady and unsteady incompressible Navier-Stokes equations. In this method, the spatial discretisation comprises an eighth-order compact scheme with stable boundary closures and a tenth-order numerical filter operator. Moreover, a Lower-Upper Symmetric Gauss-Seidel time integration method is adopted for the pseudo time sub-iteration, whereas the dual-time step method is used to improve time accuracy. The reliability of the proposed procedure is verified by simulating the phenomenon of Taylor decaying vortices, the separated flow over a backward-facing step, and the low Reynolds number steady and unsteady viscous incompressible flow over a circular cylinder. The results of the present algorithm have been proven consistent, both with exact solutions and with experimental data.
ISSN:1061-8562
1029-0257
DOI:10.1080/10618562.2012.690511