Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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26 Mar 2018
TL;DR: In this paper, a similarity solution of the lubrication equations is presented for the leveling of an interface after a hole in it closes, in agreement with experimental observations, in order to solve the leveling problem.
Abstract: A similarity solution of the lubrication equations is presented for the leveling of an interface after a hole in it closes, in agreement with experimental observations.
13 citations
TL;DR: In this article, a mixture model for the macroscopic motion of a buoyant suspension is formulated in terms of volume averaged velocities in order to ensure well-posedness of the incompressibility constraint.
13 citations
TL;DR: In this paper, the authors present new solutions to the strong explosion problem in a non-power law density profile, where the perturbations are spherically symmetric and log periodic with respect to the radius.
Abstract: We present new solutions to the strong explosion problem in a nonpower law density profile. The unperturbed self-similar solutions discovered by Waxman and Shvarts describe strong Newtonian shocks propagating into a cold gas with a density profile falling off as r^(−ω), where ω>3 (type-II solutions). The perturbations we consider are spherically symmetric and log periodic with respect to the radius. While the unperturbed solutions are continuously self-similar, the log periodicity of the density perturbations leads to a discrete self-similarity of the perturbations, i.e., the solution repeats itself up to a scaling at discrete time intervals. We discuss these solutions and verify them against numerical integrations of the time dependent hydrodynamic equations. Finally we show that this method can be generalized to treat any small, spherically symmetric density perturbation by employing Fourier decomposition.
13 citations
TL;DR: In this article, a similarity analysis of the steady free convection boundary layer over vertical and horizontal surfaces embedded in a fluid-saturated porous medium with mixed thermal boundary conditions is performed.
13 citations
TL;DR: In this paper, a nonhomogeneous and nonautonomous 2×2 quasilinear system of first order describing rate-type materials is considered within the framework of similarity reduction procedures.
Abstract: A nonhomogeneous and nonautonomous 2×2 quasilinear system of first order describing rate‐type materials is considered within the framework of similarity reduction procedures. Classes of exact similarity solutions to the governing model as well as functional forms for the material response function involved have been determined. Reductions to linear form have been carried out for different forms of constitutive laws. The present approach can be used for solving initial or boundary value problems.
13 citations