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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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Journal ArticleDOI
TL;DR: In this article, the radiation properties of an asymmetric cylinder, formed by slicing a circular cylinder with a plane making an angle π 2 − Λ with the cylinder axis, are investigated as a model problem of relevance to noise emission by novel aeroengine intakes.

24 citations

Journal ArticleDOI
TL;DR: In this article, a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions, is presented.
Abstract: We present a method for determining the linear resistive magnetohydrodynamic (MHD) stability of an axisymmetric toroidal plasma, based on the method of matched asymptotic expansions. The plasma is partitioned into a set of ideal MHD outer regions, connected through resistive MHD inner regions about singular layers where q=m/n, with m and n toroidal mode numbers, respectively, and q the safety factor. The outer regions satisfy the ideal MHD equations with zero-frequency, which are identical to the Euler-Lagrange equations for minimizing the potential energy δW. The solutions to these equations go to infinity at the singular surfaces. The inner regions satisfy the equations of motion of resistive MHD with a finite eigenvalue, resolving the singularity. Both outer and inner regions are solved numerically by newly developed singular Galerkin methods, using specialized basis functions. These solutions are matched asymptotically, providing a complex dispersion relation which is solved for global eigenvalues and...

24 citations

Journal ArticleDOI
TL;DR: It is proven that the composite optimal control can achieve a performance which is O(ee2) close to the optimal performance and the equivalence between the new composite optimal controller and the existing one is established for the standard singularly perturbed systems.
Abstract: In this paper, a new method, based on a generalized algebraic Riccati equation arising in descriptor systems, is presented to solve the composite optimal control problem of singularly perturbed systems. Contrary to the existing method, the slow subsystem is viewed as a special kind of descriptor system. A new composite optimal controller is obtained which is valid for both standard and non-standard singularly perturbed systems. It is shown that the composite optimal control can be obtained simply by revising the solution of the slow regulator problem. It is proven that the composite optimal control can achieve a performance which is O(ee2) close to the optimal performance. Although this result is well-known for the standard singularly perturbed systems, it is new in the non-standard case. The equivalence between the new composite optimal controller and the existing one is also established for the standard singularly perturbed systems.

24 citations

Book ChapterDOI
TL;DR: The history of viscous-inviscid interaction methods can be traced to the evolution of the method of matched asymptotic expansions as mentioned in this paper, and the main challenge in solving Prandtl's boundarylayer equations has been to overcome the singularity at a point of steady flow separation.
Abstract: The paper presents a personal view on the history of viscous-inviscid interaction methods, a history closely related to the evolution of the method of matched asymptotic expansions. The main challenge in solving Prandtl's boundary-layer equations has been to overcome the singularity at a point of steady flow separation. Stewartson's triple-deck theory has inspired a solution to this challenge, and thereby it paved the way for industrial use of viscous-inviscid interaction methods.

24 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835