NDLI: On Low-Dimensional Galerkin Models for Fluid Flow

Content Provider	Springer Nature Link
Author	Rempfer, D.
Copyright Year	2000
Abstract	In this paper some implications of the technique of projecting the Navier–Stokes equations onto low-dimensional bases of eigenfunctions are explored. Such low-dimensional bases are typically obtained by truncating a particularly well-suited complete set of eigenfunctions at very low orders, arguing that a small number of such eigenmodes already captures a large part of the dynamics of the system. In addition, in the treatment of inhomogeneous spatial directions of a flow, eigenfunctions that do not satisfy the boundary conditions are often used, and in the Galerkin projection the corresponding boundary conditions are ignored. We show how the restriction to a low-dimensional basis as well as improper treatment of boundary conditions can affect the range of validity of these models. As particular examples of eigenfunction bases, systems of Karhunen–Loève eigenfunctions are discussed in more detail, although the results presented are valid for any basis.
Starting Page	75
Ending Page	88
Page Count	14
File Format	PDF
ISSN	09354964
Journal	Theoretical and Computational Fluid Dynamics
Volume Number	14
Issue Number	2
e-ISSN	14322250
Language	English
Publisher	Springer-Verlag
Publisher Date	2000-06-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Fluid Flow and Transfer Processes Condensed Matter Physics Computational Mechanics

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On Low-Dimensional Galerkin Models for Fluid Flow