Chebyshev pseudospectral solution of the incompressible Navier-Stokes equations in curvilinear domains
type: Item
instance of: scholarly article
title: Chebyshev pseudospectral solution of the incompressible Navier-Stokes equations in curvilinear domains
zbMATH Open document ID: 0669.76048
DOI: 10.1016/0045-7930(88)90028-X
author: A. Farcy
author: Thierry Alziary de Roquefort
published in: Computers and Fluids
publication date: 1988-01-01T00:00:00Z
review text: A pseudospectral method for the calculation of 2-D flows of a viscous incompressible fluid in curvilinear domains is presented. The incompressible Navier-Stokes equations, expressed in terms of the primitive variables velocity and pressure, are solved in a non-orthogonal coordinate system. All the variables are expanded in double truncated series of Chebyshev polynomials. Time integration is performed by an implicit finite differences scheme for both the advective and diffusive terms. The pressure is calculated by the use of a truncated influence matrix involving all the collocation points in the field. A preconditioned iterative method is used to solve the system of linear equations resulting from the pseudospectral Chebyshev approximation. The algorithm is applied to the classical problem of the Green-Taylor vortices in order to check its accuracy; then 2 examples of viscous flow calculation are given in the case of a driven polar cavity and of a 2-D channel.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76M99
zbMATH DE Number: 4096959
zbMATH Keywords: pseudospectral method
zbMATH Keywords: 2-D flows
zbMATH Keywords: curvilinear domains
zbMATH Keywords: variables velocity and pressure
zbMATH Keywords: non-orthogonal coordinate system
zbMATH Keywords: double truncated series of Chebyshev polynomials
zbMATH Keywords: Time integration
zbMATH Keywords: implicit finite differences
zbMATH Keywords: Green-Taylor vortices
zbMATH Keywords: driven polar cavity
zbMATH Keywords: 2-D channel
MaRDI profile type: Publication
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full work available at URL: 0045-7930(88)90028-x
OpenAlex ID: W2074602688
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description: scientific article; zbMATH DE number 4096959