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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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TL;DR: In this article, an exact similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic field in the case of isothermal flow is investigated.
Abstract: Similarity solution for the propagation of a spherical shock wave in a self-gravitating perfect gas with an azimuthal magnetic field in the case of isothermal flow is investigated. The density and azimuthal magnetic field strength in the ambient medium are assumed to vary and obey power laws. An exact similarity solution obtained using the McVittie method in the case of isothermal flow is reported for the first time. The obtained solutions show that the radial fluid velocity, density, pressure, magnetic field strength, and the mass tend to zero as the point of symmetry is approached. The effects of the changes in the values of the adiabatic exponent γ and the exponent w in the variation of an initial density are considered in detail. It is shown that the magnetic field strength and mass increase with γ, whereas an increase in w exerts the reverse effect on these flow variables.

2 citations

Journal ArticleDOI
TL;DR: Turbulent mixing of two parallel similar and dissimilar fluid streams, comparing velocity and density profiles measurements with similarity solution is shown in this article, where the authors compare similarity solution with similarity measure.
Abstract: Turbulent mixing of two parallel similar and dissimilar fluid streams, comparing velocity and density profiles measurements with similarity solution

2 citations

Journal ArticleDOI
TL;DR: In this paper, the propagation of nonlinear Alfven waves in a compressible viscous fluid is described by a nonlinear diffusion equation and it is shown that it reduces to a non-linear ordinary differential equation of the first order by introducing an appropriate similarity variable.
Abstract: The propagation of nonlinear Alfven waves in a compressible viscous fluid is described by a nonlinear diffusion equation (I. Nakata: J. Phys. Soc. Jpn. 60 (1991) 1952). We show that it reduces to a nonlinear ordinary differential equation of the first order by introducing an appropriate similarity variable. The numerical solutions of the reduced equation are presented together with asymptotic solutions for both small and large Reynolds numbers.

2 citations

Journal ArticleDOI
TL;DR: In this paper, a study is undertaken to ascertain non-Newtonian effects in steady flows of elastic fluids due to an infinite rotating disk when there is suction across its surface.
Abstract: A study is undertaken to ascertain non-Newtonian effects in steady flows of elastic fluids due to an infinite rotating disk when there is suction across its surface. The fluids considered are of a class for which the similarity-type solution of von Karman is an exact solution. It is shown that the presence of elasticity (of the type considered) does not result in flow reversal, the disk acting as a centrifugal fan as in Newtonian flow.

2 citations

Posted Content
TL;DR: In this article, a new boundary methodology is presented for numerical simulation of flow of two immiscible and incompressible fluids in the presence of moving contact points. The methodology is based on combining a relation between the apparent contact angle and the contact point velocity with the similarity solution for Stokes flow at a planar interface.
Abstract: The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow. This paper presents a new boundary methodology, suitable for numerical simulation of flow of two immiscible and incompressible fluids in the presence of moving contact points. The methodology is based on combining a relation between the apparent contact angle and the contact point velocity with the similarity solution for Stokes flow at a planar interface. The relation between angle and velocity can be determined by theoretical arguments, or from simulations using a more detailed model. The approach here uses the phase field model in a micro domain, with physically relevant parameters for molecular diffusion and interface thickness. The methodology is used to formulate a new boundary condition for the velocity. Numerical results illustrate the usefulness.

2 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850