An asymptotic approach on Lagerstrom mathematical model for viscous flow at low Reynolds numbers
Abstract
An approach of using an integral equation was proposed to obtain asymptotic solutions of the problems in fluid dynamics, and has been applied to the problem at low Reynolds numbers. To show the rationality, this approach is used for the mathematical model originally proposed by Lagerstrom as a model for viscous flow at low Reynolds numbers. This twopoint boundary value problem is transformed into an integral equation which is different from that given by Cohen et al. (1978), and the inner and outer solutions are obtained from the integral representation. The basic integral equation is given by taking into account the significant degenerations of the differential operator. The present representation is more useful than Cohen's, in a sense that the lowest approximation of the inner and outer solutions are given without solving the integral equation in this problem. These asymptotic results are verified, and the rigorous proof of the existence and uniqueness of a solution is also shown.
 Publication:

Osaka Prefecture University Bulletin Series Engineering Natural Sciences
 Pub Date:
 1987
 Bibcode:
 1987BuENS..36...83K
 Keywords:

 Asymptotic Methods;
 Computational Fluid Dynamics;
 Low Reynolds Number;
 Mathematical Models;
 Viscous Flow;
 Boundary Value Problems;
 Existence Theorems;
 Integral Equations;
 Uniqueness Theorem;
 Fluid Mechanics and Heat Transfer