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 prove the existence and uniqueness of a strong solution to the stochastic Navier-Stokes equations under appropriate conditions on the data using the Galerkin approximation scheme.
Abstract: We prove the existence and uniqueness of strong solution to the stochastic Leray-
equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation scheme. We also study the asymptotic behaviour of the strong solution as alpha goes to zero. We show that a sequence of strong solutions converges in appropriate topologies to weak solutions of the 3D stochastic Navier-Stokes equations.
31 citations
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TL;DR: In this paper, the authors presented a numerical scheme for second-order time-dependent singularly perturbed reaction-diffusion problem with large delay in the undifferentiated term.
Abstract: This work presents the development of numerical scheme for second-order time-dependent singularly perturbed reaction-diffusion problem with large delay in the undifferentiated term. These t...
31 citations
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TL;DR: In this paper, the low-wavenumber structure of fixed-frequency cross-spectral density of turbulent pressure fluctuations at a rigid plane boundary is determined for flows with small but finite Mach number.
Abstract: The low‐wavenumber structure of fixed‐frequency cross‐spectral density of turbulent pressure fluctuations at a rigid plane boundary is determined for flows with small but finite Mach number. The method of matched asymptotic expansions is applied in the coordinate normal to the boundary. The boundary layer is an inner region, and prescribes an “effective” boundary velocity distribution for the outer region, which is governed by the acoustic wave equation. Those components of effective velocity with supersonic phase speeds account for the radiation of sound. For the inviscid infinite plate model, the wall‐pressure spectrum has a nonintegrable singularity at the acoustic critical wavenumber. Because of undamped contributions to point pressure from distant acoustic sources, in fact, the infinite model fails in an inviscid medium with any degree of compressibility. A large but finite model is considered, and the nonintegrable singularity at the critical wavenumber is removed. The spectrum coincides otherwise with the infinite plate result. The finite extent of the model can represent either a real geometrical limitation or the effect of damping over long distances. The intensity in the radiated field is shown to vary with the eighth power of velocity, but with a coefficient proportional to the logarithm of the characteristic in‐plane dimension.
30 citations
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TL;DR: Two complete asymptotic expansions of an integral with many simple pole singularities and a first-order, isolated saddle point evaluated by two different methods are compared in this paper, and it is shown that both expansions are exactly the same (term by term) inside and outside the transition regions.
Abstract: Two complete asymptotic expansions of an integral with many simple pole singularities and a first-order, isolated, saddle point evaluated by two different methods are compared. It is shown that both expansions are exactly the same (term by term) inside and outside the transition regions.
30 citations
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TL;DR: In this article, an upper bound for the singular perturbation parameter was derived for the uniform asymptotic stability of singularly perturbed linear time-varying systems.
Abstract: An upper bound for the singular perturbation parameter is found for the uniform asymptotic stability of singularly perturbed linear time-varying systems.
30 citations