Topic
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.
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TL;DR: In this article, the authors apply matched asymptotic expansions to the low Reynolds number flow past two parallel circular cylinders, and show that the results show fairly good agreement with Taneda's experimental data.
Abstract: Jeffery's solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to O(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda's experimental data.
28 citations
TL;DR: In this article, an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode) is carried out.
Abstract: In this paper we carry out an asymptotic analysis of the system of differential equations describing the transient behavior of a p-n-junction device (i.e., a diode). We determine the different time scales present in the equations and investigate which of them actually occur in physical situations. We derive asymptotic expansions of the solution and perform some numerical experiments.
27 citations
01 Oct 1996
TL;DR: This algorithm automatically computes the necessary asymptotic scale and does not suffer from problems of indefinite cancellation, so that an asymPTotic equivalent can always be computed for a given exp-log function.
Abstract: We give an algorithm to compute asymptotic expansions of exp-log functions. This algorithm automatically computes the necessary asymptotic scale and does not suffer from problems of indefinite cancellation. In particular, an asymptotic equivalent can always be computed for a given exp-log function.
27 citations
27 citations
TL;DR: In this article, the similarity equations for rotationally symmetric flow above an infinite counter-rotating disk are investigated both numerically and analytically, and it is deduced that there exists a critical value αcr, of α above which finite solutions are possible.
Abstract: The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcr are found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.
27 citations