A new approach in the nonlinear moment method for the Boltzmann equation

1998 ◽  
Vol 48 (S2) ◽  
pp. 281-286
Author(s):  
A. Y. Ender ◽  
I. A. Ender
Keyword(s):  
Boltzmann Equation ◽  
Moment Method ◽  
New Approach ◽  
The Boltzmann Equation

THERMAL LATTICE BOLTZMANN IN TWO DIMENSIONS

2007 ◽  
Vol 18 (04) ◽  
pp. 546-555 ◽  
Author(s):  
DIOGO NARDELLI SIEBERT ◽  
LUIZ ADOLFO HEGELE ◽  
RODRIGO SURMAS ◽  
LUÍS ORLANDO EMERICH DOS SANTOS ◽  
PAULO CESAR PHILIPPI
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Model Simulation ◽  
Physical Review ◽  
Two Dimensions ◽  
Order Of Approximation ◽  
New Approach ◽  
The Boltzmann Equation ◽  
Equilibrium Distributions ◽  
Thermal Lattice Boltzmann

The velocity discretization is a critical step in deriving the lattice Boltzmann (LBE) from the Boltzmann equation. The velocity discretization problem was considered in a recent paper (Philippi et al., From the continuous to the lattice Boltzmann equation: the discretization problem and thermal models, Physical Review E 73: 56702, 2006) following a new approach and giving the minimal discrete velocity sets in accordance with the order of approximation that is required for the LBE with respect to the Boltzmann equation. As a consequence, two-dimensional lattices and their respective equilibrium distributions were derived and discussed, considering the order of approximation that was required for the LBE. In the present work, a Chapman-Enskog (CE) analysis is performed for deriving the macroscopic transport equations for the mass, momentum and energy for these lattices. The problem of describing the transfer of energy in fluids is discussed in relation with the order of approximation of the LBE model. Simulation of temperature, pressure and velocity steps are also presented to validate the CE analysis.

Dimension-Reduced Hyperbolic Moment Method for the Boltzmann Equation with BGK-Type Collision

2014 ◽  
Vol 15 (5) ◽  
pp. 1368-1406 ◽  
Author(s):  
Zhenning Cai ◽  
Yuwei Fan ◽  
Ruo Li ◽  
Zhonghua Qiao
Keyword(s):  
Boltzmann Equation ◽  
Moment Method ◽  
Projection Algorithm ◽  
Benchmark Problems ◽  
Hermite Expansion ◽  
Globally Hyperbolic ◽  
The Boltzmann Equation ◽  
Maxwell Boundary Condition ◽  
Low Dimensional ◽  
Solution Efficiency

AbstractWe develop the dimension-reduced hyperbolic moment method for the Boltzmann equation, to improve solution efficiency using a numerical regularized moment method for problems with low-dimensional macroscopic variables and high-dimensional microscopic variables. In the present work, we deduce the globally hyperbolic moment equations for the dimension-reduced Boltzmann equation based on the Hermite expansion and a globally hyperbolic regularization. The numbers of Maxwell boundary condition required for well-posedness are studied. The numerical scheme is then developed and an improved projection algorithm between two different Hermite expansion spaces is developed. By solving several benchmark problems, we validate the method developed and demonstrate the significant efficiency improvement by dimension-reduction.

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