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, an analytical solution for laminar mudflows and debris flows that can be modeled by a Bingham-plastic law was proposed for the dam-break problem.
Abstract: An analytical solution is proposed for laminar mudflows and debris flows that can be modeled by a Bingham-plastic law. Two-dimensional, unsteady, nonuniform, Bingham flows released from a point source or a source of finite size (dam-break problem or mudslide problem) on a steep slope are considered. The method of matched asymptotic expansions was implemented to get a first-order solution. For the dam-break problem, the proposed model is found to be valid when the shock wave has advanced three reservoir lengths downstream. Also, it is found that the Bingham flow only propagates a finite distance downstream, with the shock depth asymptotically approaching the yield depth and the shock velocity asymptotically falling to zero. The hydrograph produced by a Bingham flow is seen to have a slower and lower flood peak and a longer and higher flow tail than that produced by Newtonian flow having the same dynamic viscosity. Comparison of the model predictions with laboratory observations shows reasonable agreement.
89 citations
Book•
01 Nov 1985
TL;DR: In this article, singularly perturbation analysis of nonlinear difference equations in classical form is performed in state space form and three-time-scale difference equations with application to open-loop optimal control problem.
Abstract: Singular perturbation analysis of difference equations in classical form.- Modelling and analysis of singularly perturbed difference equations in state space form.- Three-time-scale difference equations with application to open-loop optimal control problem.- Singularly perturbed nonlinear difference equations and closed-loop discrete optimal control problem.
89 citations
Journal Article•
89 citations
TL;DR: In this paper, the existence, stability, and pulse-splitting behavior of spike patterns in the one-dimensional Gray-Scott model on a finite domain is analyzed in the semi-strong spike-interaction regime.
89 citations
TL;DR: In this article, the scattering of small amplitude water waves by an array of vertical cylinders is studied theoretically and experimentally, and the energy loss due to the flow separation near the cylinders is modeled by adopting a linearized form of the quadratic resistance law.
Abstract: The scattering of small amplitude water waves by an array of vertical cylinders is studied theoretically and experimentally. In the theoretical study, a method of matched asymptotic expansions is first developed to find the reflection and the transmission coefficients without considering real fluid effects. Energy loss due to the flow separation near the cylinders is modeled by adopting a linearized form of the quadratic resistance law. It is shown that this is equivalent to introduce a complex blockage coefficient. The energy loss coefficients for square cylinders and circular cylinders are determined by comparing theoretical results with experimental data.
88 citations