scholarly journals Conjugate Solutions of Navier-Stokes Equation with Deformed Pore Structure

2014 ◽  
Vol 8 ◽  
pp. 30-48
Author(s):  
V.I. Popkov ◽  
V.I. Astafiev ◽  
V.P. Shakshin ◽  
S.V. Zatsepina
Keyword(s):  
Stokes Equation ◽  
Deformation Theory ◽  
Cluster Structure ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Porous Space ◽  
Navier Stokes Equation ◽  
Linear Solution ◽  
Regional Problems ◽  
Final Speed

Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space - to a well and from a well - to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth defluidization.

scholarly journals Global Hydrocarbon Energy Potential of Euro-Asia or Solution of Navier-Stokes Equation for Deformed Micro-Structure of the Earth’s Porous Space

2015 ◽  
Vol 9 (9) ◽  
Author(s):  
Vyacheslav I. Popkov ◽  
Vladimir I. Astafiev ◽  
M. Shterenberg ◽  
Ilus G. Khamitov ◽  
Vladimir A. Kolesnikov ◽  
...  
Keyword(s):  
Stokes Equation ◽  
Navier Stokes ◽  
Porous Space ◽  
Micro Structure ◽  
Energy Potential ◽  
Navier Stokes Equation

scholarly journals Basics of Fluid Dynamics

2021 ◽  
Author(s):  
Nahom Alemseged Worku
Keyword(s):  
Stokes Equation ◽  
Incompressible Flows ◽  
Mass Conservation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Conservation Of Energy ◽  
Conservation Of Momentum ◽  
Almost All ◽  
Transport Theorem

In this chapter, studies on basic properties of fluids are conducted. Mathematical and scientific backgrounds that helps sprint well into studies on fluid mechanics is provided. The Reynolds Transport theorem and its derivation is presented. The well-known Conservation laws, Conservation of Mass, Conservation of Momentum and Conservation of Energy, which are the foundation of almost all Engineering mechanics simulation are derived from Reynolds transport theorem and through intuition. The Navier–Stokes equation for incompressible flows are fully derived consequently. To help with the solution of the Navier–Stokes equation, the velocity and pressure terms Navier–Stokes equation are reduced into a vorticity stream function. Classification of basic types of Partial differential equations and their corresponding properties is discussed. Finally, classification of different types of flows and their corresponding characteristics in relation to their corresponding type of PDEs are discussed.

Wavelet-distributed approximating functional method for solving the Navier-Stokes equation

1998 ◽  
Vol 115 (1) ◽  
pp. 18-24 ◽  
Author(s):  
G.W. Wei ◽  
D.S. Zhang ◽  
S.C. Althorpe ◽  
D.J. Kouri ◽  
D.K. Hoffman
Keyword(s):  
Stokes Equation ◽  
Functional Method ◽  
Navier Stokes ◽  
Navier Stokes Equation

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

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