Global solutions for the one-dimensional compressible Navier-Stokes-Smoluchowski system

2017 ◽  
Vol 58 (5) ◽  
pp. 051502 ◽  
Author(s):  
Jianlin Zhang ◽  
Changming Song ◽  
Hong Li
Keyword(s):  
Global Solutions ◽  
Navier Stokes ◽  
One Dimensional ◽  
The One

Global Solutions to the One-Dimensional Compressible Navier--Stokes--Poisson Equations with Large Data

2013 ◽  
Vol 45 (2) ◽  
pp. 547-571 ◽  
Author(s):  
Zhong Tan ◽  
Tong Yang ◽  
Huijiang Zhao ◽  
Qingyang Zou
Keyword(s):  
Global Solutions ◽  
Large Data ◽  
Navier Stokes ◽  
One Dimensional ◽  
Poisson Equations ◽  
The One

Asymptotics toward a nonlinear wave for an outflow problem of a model of viscous ions motion

2017 ◽  
Vol 27 (11) ◽  
pp. 2111-2145 ◽  
Author(s):  
Yeping Li ◽  
Peicheng Zhu
Keyword(s):  
Nonlinear Wave ◽  
The Self ◽  
Navier Stokes ◽  
Asymptotically Stable ◽  
Spatial Decay ◽  
Main Ingredient ◽  
One Dimensional ◽  
Poisson Equations ◽  
Self Consistent ◽  
The One

We shall investigate the asymptotic stability, toward a nonlinear wave, of the solution to an outflow problem for the one-dimensional compressible Navier–Stokes–Poisson equations. First, we construct this nonlinear wave which, under suitable assumptions, is the superposition of a stationary solution and a rarefaction wave. Then it is shown that the nonlinear wave is asymptotically stable in the case that the initial data are a suitably small perturbation of the nonlinear wave. The main ingredient of the proof is the [Formula: see text]-energy method that takes into account both the effect of the self-consistent electrostatic potential and the spatial decay of the stationary part of the nonlinear wave.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

2021 ◽  
pp. 54-58
Author(s):  
E.M. Zveriaev ◽  
Keyword(s):  
Stokes Equations ◽  
Asymptotic Series ◽  
Viscous Friction ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Dimensional Theory ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Beam Oscillation

Abstract. On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

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