A pseudospectral method for the solution of the two-dimensional Navier-Stokes equations in the primitive variable formulation

A pseudospectral method was developed for the solution of the Navier-Stokes equations for incompressible flows in the primitive-variable formulation. The method employs Chebyshev expansion methods in order to generate approximations to the momentum and pressure equtions and utilizes a well-known fra...

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Bibliographic Details
Published in:Journal of computational physics 1986-12, Vol.67 (2), p.361-371
Main Authors: Hatziavramidis, Dimitri, Ku, Hwar-Ching
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Other techniques and industries
Physics
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Summary:A pseudospectral method was developed for the solution of the Navier-Stokes equations for incompressible flows in the primitive-variable formulation. The method employs Chebyshev expansion methods in order to generate approximations to the momentum and pressure equtions and utilizes a well-known fractional time-step procedure in obtaining a solution to these equations. Results for the buoyancy-driven flow in a square enclosure with nonisothermal vertical and insulated horizontal walls, at Rayleigh numbers in the range 1.4 × 10 4–1.4 × 10 6, are represented. The proposed method is easy to implement and can accurately reproduce the physics of the flow under consideration from transient to steady state.
ISSN:0021-9991
1090-2716
DOI:10.1016/0021-9991(86)90268-8