scholarly journals A kinetic theory solution method for the Navier-Stokes equations

1993 ◽  
Vol 17 (3) ◽  
pp. 177-193 ◽  
Author(s):  
M. N. Macrossan ◽  
R. I. Oliver
Keyword(s):  
Kinetic Theory ◽  
Solution Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Theory Solution

Implicit solution method for incompressible Navier-Stokes equations including two-layer k-tau turbulence model

AIAA Journal ◽  
1996 ◽  
Vol 34 (12) ◽  
pp. 2501-2508 ◽  
Author(s):  
Jurg Kuffer ◽  
Bernhard Muller ◽  
Torstein K. Fannelop
Keyword(s):  
Turbulence Model ◽  
Solution Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Illusions of Elastic Collisions in the Sciences:

2020 ◽  
Vol 5 (1) ◽  
pp. 87-90
Author(s):  
Kent W. Mayhew
Keyword(s):  
Statistical Theory ◽  
Kinetic Theory ◽  
Stokes Equations ◽  
Inelastic Collisions ◽  
Navier Stokes ◽  
Lagrangian Mechanics ◽  
Navier Stokes Equations ◽  
Elastic Collisions

Employing elastic collisions rather than the reality of inelastic collisions simplifies much of the theoretical sciences. The consequences of such simplification is completely ignored/unrealized by the majority, hence must be addressed. At the crux of the problem is arguably the illusion of elastic collisions in kinetic theory, but this extends to other realms of physics including statistical theory, Lagrangian mechanics and the Navier-Stokes equations.

On the initial-value problem in the kinetic theory of gases

1971 ◽  
Vol 50 (2) ◽  
pp. 271-284 ◽  
Author(s):  
Howard R. Baum
Keyword(s):  
Kinetic Theory ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Mean Free Path ◽  
Spatial Dimension ◽  
Collision Integral ◽  
Navier Stokes ◽  
Kinetic Theory Of Gases ◽  
Navier Stokes Equations ◽  
Scale Perturbation

The relaxation of an initially non-uniform gas to equilibrium is studied within the framework of the kinetic theory of gases. The macroscopic gas properties are taken to depend on one spatial dimension as well as the time. The amplitude of the non-uniformity is assumed to be small with a length scale large compared with the mean free path, and the Krook model of the Boltzmann collision integral is employed.By applying multi-time scale perturbation methods to this reduced problem, uniformly valid analytical solutions for the macroscopic velocity, density and temperature are obtained. The macroscopic equations appropriate to each stage of the relaxation process are obtained in a straightforward and unambiguous manner. The distribution function obtained is shown to be a re-expansion of the Chapman–Enskog solution of the Krook equation, with additional terms accounting for the relaxation of the initial conditions to a near equilibrium form. The results indicate that the uniformly valid frst approximation to the macroscopic velocity, density and temperature can be obtained from the Navier–Stokes equations, but that no purely macroscopic set of equations will suffice for the determination of higher approximations.

A Simultaneous Variable Solution Procedure for Laminar and Turbulent Flows in Curved Channels and Bends

2000 ◽  
Vol 122 (3) ◽  
pp. 552-559 ◽  
Author(s):  
Jianrong Wang ◽  
Siamack A. Shirazi
Keyword(s):  
Experimental Data ◽  
Numerical Solution ◽  
Numerical Method ◽  
Solution Method ◽  
Stokes Equations ◽  
Turbulence Models ◽  
Solution Procedure ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Curved Channels

Direct Numerical Simulation of turbulent flow requires accurate numerical techniques for solving the Navier-Stokes equations. Therefore, the Navier-Stokes equations in general orthogonal and nonorthogonal coordinates were employed and a simultaneous variable solution method was extended to solve these general governing equations. The present numerical method can be used to accurately predict both laminar and turbulent flow in various curved channels and bends. To demonstrate the capability of this numerical method and to verify the method, the time-averaged Navier-Stokes equations were employed and several turbulence models were also implemented into the numerical solution procedure to predict flows with strong streamline curvature effects. The results from the present numerical solution procedure were compared with available experimental data for a 90 deg bend. All of the turbulence models implemented resulted in predicted velocity profiles which were in agreement with the trends of experimental data. This indicates that the solution method is a viable numerical method for calculating complex flows. [S0098-2202(00)01803-4]

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