Exact solution for the spatially homogeneous nonlinear Kac model of the Boltzmann equation with an external force term

1984 ◽  
Vol 17 (11) ◽  
pp. 2355-2361 ◽  
Author(s):  
H Cornille
Keyword(s):  
Exact Solution ◽  
Boltzmann Equation ◽  
External Force ◽  
Force Term ◽  
The Boltzmann Equation ◽  
Kac Model ◽  
Spatially Homogeneous

scholarly journals SECOND-ORDER SCHEME FOR THE SPATIALLY HOMOGENEOUS BOLTZMANN EQUATION WITH MAXWELLIAN MOLECULES

1996 ◽  
Vol 06 (01) ◽  
pp. 137-147 ◽  
Author(s):  
JENS STRUCKMEIER ◽  
KONRAD STEINER
Keyword(s):  
Boltzmann Equation ◽  
Particle Method ◽  
Time Discretization ◽  
Second Order ◽  
Particle Methods ◽  
Homogeneous Boltzmann Equation ◽  
The Boltzmann Equation ◽  
Spatially Homogeneous ◽  
Maxwellian Molecules ◽  
Spatially Homogeneous Boltzmann Equation

In the standard approach particle methods for the Boltzmann equation are obtained using an explicit time discretization of the spatially homogeneous Boltzmann equation. This kind of discretization leads to a restriction on the discretization parameter as well as on the differential cross-section in the case of the general Boltzmann equation. Recently, construction of an implicit particle scheme for the Boltzmann equation with Maxwellian molecules was shown. This paper combines both approaches using a linear combination of explicit and implicit discretizations. It is shown that the new method leads to a second-order particle method when using an equiweighting of explicit and implicit discretization.

On the initial value problem for the Boltzmann equation with a force term

1989 ◽  
Vol 18 (1) ◽  
pp. 87-102 ◽  
Author(s):  
N. Bellomo ◽  
M. Lachowicz ◽  
A. Palczewski ◽  
G. Toscani
Keyword(s):  
Boltzmann Equation ◽  
Initial Value Problem ◽  
Force Term ◽  
Initial Value ◽  
The Boltzmann Equation

Fick's First Law Correction by an exact solution of the boltzmann equation

1987 ◽  
Vol 12 (3) ◽  
pp. 105-112 ◽  
Author(s):  
D. Straub ◽  
R. Graue ◽  
F. Heitmeir ◽  
P. Nebendahl ◽  
Th. K. Wurst
Keyword(s):  
Exact Solution ◽  
Boltzmann Equation ◽  
The Boltzmann Equation
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