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, a method of approximate potential symmetries for partial differential equations with a small parameter is introduced, by writing a given perturbed partial differential equation R in a conserved form, an associated system with potential variables as additional variables is obtained.
Abstract: The method of approximate potential symmetries for partial differential equations with a small parameter is introduced. By writing a given perturbed partial differential equation R in a conserved form, an associated system S with potential variables as additional variables is obtained. Approximate Lie point symmetries admitted by S induce approximate potential symmetries of R. As applications of the theory, approximate potential symmetries for a perturbed wave equation with variable wave speed and a nonlinear diffusion equation with perturbed convection terms are obtained. The corresponding approximate group-invariant solutions are also derived.
43 citations
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TL;DR: In this article, asymptotic expansions are given for the q-gamma function, the q -exponential functions, and for the Hahn-Exton q -Bessel function.
43 citations
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TL;DR: In this article, a detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number is given, where the analysis resorts to the method of matched asymptotic expansions.
Abstract: The primary objective of this paper is to obtain the detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number. Attention is paid to the shape effects due to the flattening of the cylinder and to the inertial effects of the fluid. The analysis resorts to the method of matched asymptotic expansions. The main part of the inner expansion describes the near flow field as a Stokes flow, which is characterized by the singularities arranged at the two foci of the ellipse. The first three terms = Reynolds number) in the inner expansion are developed, and the flow aspects under the influence of the fluid inertia are investigated. The streamline patterns with one or two vortices round a finite flat plate of zero thickness, which is a special case of the elliptic cylinder, are presented.
43 citations
01 Jan 2016
42 citations
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TL;DR: In this paper, the Navier boundary condition is replaced by a boundary condition which attempts to account for boundary slip due to the tangential shear at the boundary, where the slip length l is made dimensionless with respect to the corresponding radius.
Abstract: For micro- and nanoscale problems, boundary surface roughness often means that the usual no-slip boundary condition of fluid mechanics does not apply. Here we examine the steady low-Reynolds-number flow past a nanosphere and a circular nanocylinder in a Newtonian fluid, with the no-slip boundary condition replaced by a boundary condition which attempts to account for boundary slip due to the tangential shear at the boundary. We apply the so-called Navier boundary condition and use the method of matched asymptotic expansions. This model possesses a single parameter to account for the slip, the slip length l, which is made dimensionless with respect to the corresponding radius, which is assumed to be of the same order of magnitude as the slip length. Numerical results are presented for the two extreme cases, l = 0 corresponding to classical theory, and l → ∞ corresponding to complete slip. The streamlines for l > 0 are closer to the body than for l = 0, while the frictional drag for l > 0 is reduced below the values for l = 0, as might be expected. For the circular cylinder, results corresponding to l → ∞ are in complete accord with certain low-Reynolds-number experimental results, and this excellent agreement is much better than that predicted by the no-slip boundary condition.
42 citations