scholarly journals A random discrete velocity model and approximation of the Boltzmann equation

1993 ◽  
Vol 70 (3-4) ◽  
pp. 773-792 ◽  
Author(s):  
Reinhard Illner ◽  
Wolfgang Wagner
Keyword(s):  
Boltzmann Equation ◽  
Velocity Model ◽  
Discrete Velocity ◽  
The Boltzmann Equation ◽  
Discrete Velocity Model

scholarly journals On the Generation of a Hexagonal Collision Model for the Boltzmann equation

2004 ◽  
Vol 4 (3) ◽  
pp. 271-289 ◽  
Author(s):  
Laek S. Andallan
Keyword(s):  
Boltzmann Equation ◽  
Velocity Model ◽  
Numerical Results ◽  
Hexagonal Grid ◽  
Collision Model ◽  
Discrete Velocity ◽  
The Boltzmann Equation ◽  
Discrete Velocity Model

AbstractIn this article we prove the existence of two different classes of regular hexagons in the hexagonal grid. We develop a generalized layer-wise construction of a hexagonal discrete velocity model and derive general formulae to identify all regular hexagons belonging to the grid. We also present some numerical results based on the hexagonal grid.

A Consistency Result for a Discrete-Velocity Model of the Boltzmann Equation

1997 ◽  
Vol 34 (5) ◽  
pp. 1865-1883 ◽  
Author(s):  
Andrzej Palczewski ◽  
Jacques Schneider ◽  
Alexandre V. Bobylev
Keyword(s):  
Boltzmann Equation ◽  
Velocity Model ◽  
Discrete Velocity ◽  
The Boltzmann Equation ◽  
Discrete Velocity Model

Monte Carlo solution of the Boltzmann equation via a discrete velocity model

2011 ◽  
Vol 230 (4) ◽  
pp. 1265-1280 ◽  
Author(s):  
A.B. Morris ◽  
P.L. Varghese ◽  
D.B. Goldstein
Keyword(s):  
Monte Carlo ◽  
Boltzmann Equation ◽  
Velocity Model ◽  
Discrete Velocity ◽  
The Boltzmann Equation ◽  
Discrete Velocity Model

Study of rarefied shear flow by the discrete velocity method

1964 ◽  
Vol 19 (3) ◽  
pp. 401-414 ◽  
Author(s):  
James E. Broadwell
Keyword(s):  
Shear Stress ◽  
Boltzmann Equation ◽  
Fluid Velocity ◽  
Velocity Model ◽  
Low Mach Number ◽  
Discrete Velocity ◽  
Moment Methods ◽  
Discrete Velocity Method ◽  
Finite Set ◽  
Discrete Velocity Model

The application of a simple discrete velocity model to low Mach number Couette and Rayleigh flow is investigated. In the model, the molecular velocities are restricted to a finite set and in this study only eight equal speed velocities are allowed. The Boltzmann equation is reduced by this approximation to a set of coupled differential equations which can be solved in closed form. The fluid velocity and shear stress in Couette flow are in approximate accord with those of Wang Chang & Uhlenbeck (1954) and of Lees (1959) over the complete range of Knudsen number. Similarly, the Rayleigh flow solution is remarkably like those found by other investigators using moment methods.

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