Comparison of numerical solutions of the Navier?Stokes equations and a kinetic model in the one-dimensional case

1980 ◽  
Vol 15 (5) ◽  
pp. 752-755 ◽  
Author(s):  
A. A. Makhmudov ◽  
S. P. Popov
Keyword(s):  
Kinetic Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One

scholarly journals NEWTONIAN FLOW IN CONVERGING-DIVERGING CAPILLARIES

2013 ◽  
Vol 04 (03) ◽  
pp. 1350011 ◽  
Author(s):  
TAHA SOCHI
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Navier Stokes ◽  
Lubrication Approximation ◽  
Newtonian Flow ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Analytical Expressions

The one-dimensional Navier–Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier–Stokes are identical to those obtained from the lubrication approximation within a nondimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

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.

Cauchy problem for the one-dimensional compressible Navier-Stokes equations

2012 ◽  
Vol 32 (1) ◽  
pp. 315-324 ◽  
Author(s):  
Lian Ruxu ◽  
Liu Jian ◽  
Li Hailiang ◽  
Xiao Ling
Keyword(s):  
Cauchy Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One

scholarly journals Analytic and Numerical Solutions of Couette Flow Problem: A Comparative Study

2017 ◽  
Vol 12 (1) ◽  
pp. 105-113
Author(s):  
Dhak Bahadur Thapa ◽  
Kedar Nath Uprety
Keyword(s):  
Differential Equation ◽  
Couette Flow ◽  
Numerical Solutions ◽  
Flow Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Parabolic Partial Differential Equation ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Nicolson Scheme

In this work, an incompressible viscous Couette flow is derived by simplifying the Navier-Stokes equations and the resulting one dimensional linear parabolic partial differential equation is solved numerically employing a second order finit difference Crank-Nicolson scheme. The numerical solution and the exact solution are presented graphically.Journal of the Institute of Engineering, 2016, 12(1): 105-113

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