Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Similarity solutions of the navierstokes equations

Abstract: Similarity solutions of the Navier-Stokes equations are reviewed. It is shownthat the method of stretching leads to all existing significant nonlinear solutions. The steady state solutions are either inversely proportional or proportional to distance. The unsteady solutions have a very specific time dependence.

Similarity solution using group theoretic method for unsteady flow behind shock wave in a self-gravitating dusty gas

Abstract: In this article, the similarity solution using the Lie group theoretic method for unsteady isothermal and adiabatic flows behind cylindrical or spherical shock wave in a mixture of self-gravitating real gas and small solid particles is discussed. The Lie group theoretic method gives out different cases, i.e., exponential law and power-law shock paths. The similarity solution exists only when the shock path varies according to an exponential law. The dispersal of the flow variables with the variations of the solid particles’ mass concentration in the mixture kp, gravitational parameter g0, the ratio of the density of solid particles to the initial density of the gas μ1, non-idealness parameter b¯ and the geometry index ν are discussed graphically. It is found that an increase in the value of μ1 or g0 or ν leads to an increase in the shock strength, but the shock wave decay with an increase in b¯. A comparison between the solutions for cylindrical and spherical symmetry, and for adiabatic and isothermal flows is also made.

Self‐similar solutions for axisymmetric jets using two turbulence models

Abstract: Similarity solutions for incompressible axisymmetric jets using a k–ϵ and a constant eddy diffusivity turbulence models are considered. For the k–ϵ model, the governing equations are very complex. Therefore, a transformation that simplifies these equations and makes them amenable to efficient numerical solution is used. Results for the velocity, turbulent kinetic energy and dissipation rate are obtained. Also, velocity decay rate, growth rate, entrainment and kinetic energy decay rate are determined. A comparison with experimental data and other works utilizing a parabolic marching asymptotic solution to the full partial differential equations is made. This comparison shows that similarity solutions are more accurate than solutions using numerical marching procedures.