scholarly journals Boundary Layers and Shock Profiles for the Broadwell Model

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Niclas Bernhoff
Keyword(s):  
Boltzmann Equation ◽  
Boundary Layers ◽  
Nonlinear Problem ◽  
Nonlinear Boundary ◽  
Velocity Model ◽  
Discrete Velocity ◽  
Shock Profiles ◽  
Discrete Velocity Model ◽  
Good Agreement ◽  
Discrete Boltzmann Equation

We consider the existence of nonlinear boundary layers and the typically nonlinear problem of existence of shock profiles for the Broadwell model, which is a simplified discrete velocity model for the Boltzmann equation. We find explicit expressions for the nonlinear boundary layers and the shock profiles. In spite of the few velocities used for the Broadwell model, the solutions are (at least partly) in qualitatively good agreement with the results for the discrete Boltzmann equation, that is the general discrete velocity model, and the full Boltzmann equation.

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.

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

EXACT (1+1)-DIMENSIONAL SOLUTIONS TO A DISCRETE VELOCITY MODEL FOR COAGULATION-FRAGMENTATION

1994 ◽  
Vol 04 (06) ◽  
pp. 857-869
Author(s):  
M. IKLÉ
Keyword(s):  
Boltzmann Equation ◽  
Computer Algebra ◽  
Hyperbolic Equations ◽  
Velocity Model ◽  
Inelastic Collisions ◽  
Computer Algebra Systems ◽  
Particle Coagulation ◽  
Discrete Velocity ◽  
Velocity Models ◽  
Discrete Velocity Model

A family of discrete velocity models is proposed for the study of particle coagulation and fragmentation in gases. Patterned after the Broadwell model, the models allow inelastic collisions to occur, as well as elastic collisions. The models generate systems of highly coupled semilinear hyperbolic equations which approximate the Boltzmann equation. With the aid of the powerful computer algebra systems Mathematica and Maple, we find an exact four-parameter solution to the simplest model.

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