scholarly journals Asymptotic Solutions of the Kinetic Boltzmann Equation and Multicomponent Non-Equilibrium Gas Dynamics

2016 ◽  
Vol 04 (08) ◽  
pp. 1687-1697
Author(s):  
S. A. Serov ◽  
S. S. Serova
Keyword(s):  
Boltzmann Equation ◽  
Gas Dynamics ◽  
Asymptotic Solutions ◽  
Kinetic Boltzmann Equation ◽  
Non Equilibrium

THE CONTRIBUTION OF THE BHATNAGAR–GROSS–KROOK MODEL TO THE DEVELOPMENT OF RAREFIED GAS DYNAMICS IN THE EARLY YEARS OF THE SPACE AGE

2013 ◽  
Vol 25 (01) ◽  
pp. 1340025
Author(s):  
RODDAM NARASIMHA
Keyword(s):  
Boltzmann Equation ◽  
Gas Dynamics ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Early Years ◽  
Plane Shock ◽  
Bgk Model ◽  
The Boltzmann Equation ◽  
Nonequilibrium Flows ◽  
Space Age

The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.

Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

2019 ◽  
Vol 34 (3) ◽  
pp. 143-150
Author(s):  
Sergey V. Rogasinsky
Keyword(s):  
Boltzmann Equation ◽  
Projection Method ◽  
Orthonormal Basis ◽  
Statistical Modelling ◽  
Hermite Functions ◽  
Nonlinear Boltzmann Equation ◽  
Kinetic Boltzmann Equation ◽  
Relaxation Problem ◽  
Nonlinear Kinetic ◽  
Approximation Of A Function

Abstract The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

scholarly journals Simulation of non-equilibrium gas kinetic processes in the multitube Knudsen pump on the basis of the Boltzmann equation

2020 ◽  
Vol 1560 ◽  
pp. 012061
Author(s):  
Kloss Yu Yu ◽  
F G Tcheremissine ◽  
M Yu Shirkin ◽  
I V Govorun ◽  
V Shirokovskaya Yu
Keyword(s):  
Boltzmann Equation ◽  
The Boltzmann Equation ◽  
Kinetic Processes ◽  
Knudsen Pump ◽  
Non Equilibrium
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