期刊
THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS
卷 14, 期 2, 页码 75-88出版社
SPRINGER VERLAG
DOI: 10.1007/s001620050131
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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-Loeve eigenfunctions are discussed in more detail, although the results presented are valid for any basis.
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