The Uniqueness of Weak Solutions of the One‐Dimensional Scalar Analog to the Navier‐Stokes Equation

1964 ◽  
Vol 5 (9) ◽  
pp. 1290-1292
Author(s):  
Edgar A. Kraut
Keyword(s):  
Stokes Equation ◽  
Weak Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
The One ◽  
Scalar Analog

scholarly journals Local Exact Controllability for the One-Dimensional Compressible Navier–Stokes Equation

2012 ◽  
Vol 206 (1) ◽  
pp. 189-238 ◽  
Author(s):  
Sylvain Ervedoza ◽  
Olivier Glass ◽  
Sergio Guerrero ◽  
Jean-Pierre Puel
Keyword(s):  
Stokes Equation ◽  
Exact Controllability ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
The One

scholarly journals Simple parametrization methods for generating Adomian polynomials

2016 ◽  
Vol 10 (1) ◽  
pp. 168-185 ◽  
Author(s):  
K.K. Kataria ◽  
P. Vellaisamy
Keyword(s):  
Explicit Expression ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Nonlinear Operators ◽  
Adomian Polynomials ◽  
The One

In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.

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.

scholarly journals Splitting Decomposition Homotopy Perturbation Method To Solve One -Dimensional Navier -Stokes Equation

2017 ◽  
Vol 13 (2) ◽  
pp. 7123-7134 ◽  
Author(s):  
A. S. J Al-Saif ◽  
Takia Ahmed J Al-Griffi
Keyword(s):  
Exact Solution ◽  
Stokes Equation ◽  
Homotopy Perturbation Method ◽  
Differential Operators ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
Splitting Time

We have proposed in this  research a new scheme to find analytical  approximating solutions for Navier-Stokes equation  of  one  dimension. The  new  methodology depends on combining  Adomian  decomposition  and Homotopy perturbation methods  with the splitting time scheme for differential operators . The new methodology is applied on two problems of  the test: The first has an exact solution  while  the other one has no  exact solution. The numerical results we  obtained  from solutions of two problems, have good convergent  and high  accuracy   in comparison with the two traditional Adomian  decomposition  and Homotopy  perturbationmethods . 

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