Method of matched asymptotic expansions

About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.

On The Role of a Non-Newtonian Fluid in Short Bearing Theory

Abstract: The importance of rheological properties of lubricants has arisen from the realization that non-Newtonian fluid effects are manifested over a broad range of lubrication applications. In this paper a theoretical investigation of short journal bearings performance characteristics for non-Newtonian power-law lubricants is given. A modified form of the Reynolds’ equation for hydrodynamic lubrication is studied in the asymptotic limit of small slenderness ratio (i.e., bearing length to diameter, L/D = λ→0). Fluid film pressure distributions in short bearings of arbitrary azimuthal length are studied using matched asymptotic expansions in the slenderness ratio. The merit of the short bearing approach used in solving a modified Reynolds’ equation by the method of matched asymptotic expansions is emphasized. Fluid film pressure distributions are determined without recourse to numerical solutions to a modified Reynolds’ equation. Power-law rheological exponents less than and equal to one are considered; power-law fluids exhibit reduced load capacities relative to the Newtonian fluid. The cavitation boundary shape is determined from Reynolds’ free surface condition; and the boundary shape is shown to be independent of the bearing eccentricity ratio.

Interior Layers for Second-Order Singular Equations

Abstract: Our aim in this article is to study singularly perturbed problems which display boundary layers in the interior of the domain. These interior boundary layers which supplement the usual boundary layers at the boundary, are generated by discontinuities in the data. Second-order linear elliptic one-dimensional and multi-dimensional problems are considered in this article.

Viscous-inviscid interactions on axisymmetric bodies of revolution in supersonic flow

Abstract: Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and inviscid supersonic external flows is investigated in the limit of large Reynolds numbers. The resulting triple-deck equations are solved numerically for two different cases of body shapes: a cylinder-cone configuration and a configuration consisting of two concentric cylinders which are connected by a smooth curve. Solutions to the linearized as well as the fully nonlinear equations are presented.

Averaging a Singularly Perturbed Equation with Rapidly Oscillating Coefficients in a Layer

Abstract: A complete asymptotic expansion is constructed for a second-order equation of elliptic type with a small parameter in the highest-order derivative and rapidly oscillating coefficients.Bibliography: 11 titles.