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Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations

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Pinelli, Alfredo and Vacca, A. (1994) Chebyshev collocation method and multidomain decomposition for the incompressible Navier‐Stokes equations. International journal for numerical methods in fluids, 18 (8). pp. 781-799. ISSN 0271-2091

Official URL: http://onlinelibrary.wiley.com/doi/10.1002/fld.1650180806/pdf


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Abstract

The two-dimensional incompressible Navier-Stokes equations in primitive variables have been solved by a pseudospectral Chebyshev method using a semi-implicit fractional step scheme. The latter has been adapted to the particular features of spectral collocation methods to develop the monodomain algorithm. In particular, pressure and velocity collocated on the same nodes are sought in a polynomial space of the same order; the cascade of scalar elliptic problems arising after the spatial collocation is solved using finite difference preconditioning. With the present procedure spurious pressure modes do not pollute the pressure field.

As a natural development of the present work a multidomain extent was devised and tested. The original domain is divided into a union of patching sub-rectangles. Each scalar problem obtained after spatial collocation is solved by iterating by subdomains. For steady problems a C1 solution is recovered at the interfaces upon convergence, ensuring a spectrally accurate solution.

A number of test cases have been solved to validate the algorithm in both its single-block and multidomain configurations.

The preliminary results achieved indicate that collocation methods in multidomain configurations might become a viable alternative to the spectral element technique for accurate flow prediction.


Item Type:Article
Uncontrolled Keywords:Incompressible Navier-Stokes; collocated Chebyshev schemes; domain decomposition
Subjects:Sciences > Physics
ID Code:21892
Deposited On:17 Jun 2013 09:05
Last Modified:12 Dec 2018 15:08

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