Distribution Patterns of Eigenvalues of Laminar Pipe Flows (1st Report, Determination of Approximate Subspace in the Galerkin Method)

Tadaya Ito, Kenji Hase, Yoshikazu Suematsu, Toshiyuki Hayase

Research output: Contribution to journalArticlepeer-review

Abstract

As the first step in clarifying the structure and dynamic behavior of a linear system which describes the perturbation of a parallel flow in a pipe, the distribution of the eigenvalues in the system is studied. For this purpose, first the formulation is made in a Hilbert space, which facilitates the geometrical interpretation of the problem. Then, by applying the Galerkin method, a finite dimensional approximate linear system is obtained. In the latter process, a difficulty arises as to how the order of the approximation is to be determined. To give an answer to this, a concrete measure is proposed using the concept of the operator invariance of the subspace. To examine the validity of the measure, the distribution of the eigenvalues of Poiseuille flow is calculated. It is found that the proposed measure is a dequate for obtaining the accurate distribution of the eigenvalues.

Original languageEnglish
Pages (from-to)1917-1924
Number of pages8
JournalTransactions of the Japan Society of Mechanical Engineers Series B
Volume53
Issue number491
DOIs
Publication statusPublished - 1987

Keywords

  • Distribution of Eigenvalues
  • Eigenvalue Problem
  • Fluid Mechanics
  • Galerkin Method
  • Laminar Pipe Flow

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering

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