TY - JOUR

T1 - Distribution Patterns of Eigenvalues of Laminar Pipe Flows (1st Report, Determination of Approximate Subspace in the Galerkin Method)

AU - Ito, Tadaya

AU - Hase, Kenji

AU - Suematsu, Yoshikazu

AU - Hayase, Toshiyuki

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

KW - Distribution of Eigenvalues

KW - Eigenvalue Problem

KW - Fluid Mechanics

KW - Galerkin Method

KW - Laminar Pipe Flow

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U2 - 10.1299/kikaib.53.1917

DO - 10.1299/kikaib.53.1917

M3 - Article

AN - SCOPUS:0023116322

VL - 53

SP - 1917

EP - 1924

JO - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B

JF - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B

SN - 0387-5016

IS - 491

ER -