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CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter.

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Title: CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter.
Authors: Codina, R.1, Zienkiewicz, O. C.2
Source: Communications in Numerical Methods in Engineering. Feb2002, Vol. 18 Issue 2, p99-112. 14p. 1 Diagram.
Subjects: Galerkin methods, Numerical analysis, Navier-Stokes equations, Finite element method, Least squares
Abstract: In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier–Stokes equations. The first is the characteristic-based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The second approach is the Galerkin-least-squares (GLS) method, in which a least-squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter.
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  Data: <searchLink fieldCode="JN" term="%22Communications+in+Numerical+Methods+in+Engineering%22">Communications in Numerical Methods in Engineering</searchLink>. Feb2002, Vol. 18 Issue 2, p99-112. 14p. 1 Diagram.
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  Data: In this work we compare two apparently different stabilization procedures for the finite element approximation of the incompressible Navier–Stokes equations. The first is the characteristic-based split (CBS). It combines the characteristic Galerkin method to deal with convection dominated flows with a classical splitting technique, which in some cases allows us to use equal velocity–pressure interpolations. The second approach is the Galerkin-least-squares (GLS) method, in which a least-squares form of the element residual is added to the basic Galerkin equations. It is shown that both formulations display similar stabilization mechanisms, provided the stabilization parameter of the GLS method is identified with the time step of the CBS approach. This identification can be understood from a formal Fourier analysis of the linearized problem. Copyright © 2001 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Communications in Numerical Methods in Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Navier-Stokes equations
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