scholarly journals Computational framework for the regularized 20-moment equations for non-equilibrium gas flows

2008 ◽  
Vol 56 (8) ◽  
pp. 1433-1439 ◽  
Author(s):  
S. Mizzi ◽  
X. J. Gu ◽  
D. R. Emerson ◽  
R. W. Barber ◽  
J. M. Reese
Keyword(s):  
Gas Flows ◽  
Moment Equations ◽  
Computational Framework ◽  
Non Equilibrium

On Singular Closures for the 5-Moment System in Kinetic Gas Theory

2015 ◽  
Vol 17 (2) ◽  
pp. 371-400 ◽  
Author(s):  
Roman Pascal Schaerer ◽  
Manuel Torrilhon
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Second Order ◽  
Gas Flows ◽  
Moment Equations ◽  
Moment System ◽  
Entropy Principle ◽  
Kinetic Gas Theory ◽  
Closure Theory ◽  
Non Equilibrium

AbstractMoment equations provide a flexible framework for the approximation of the Boltzmann equation in kinetic gas theory. While moments up to second order are sufficient for the description of equilibrium processes, the inclusion of higher order moments, such as the heat flux vector, extends the validity of the Euler equations to non-equilibrium gas flows in a natural way.Unfortunately, the classical closure theory proposed by Grad leads to moment equations, which suffer not only from a restricted hyperbolicity region but are also affected by non-physical sub-shocks in the continuous shock-structure problem if the shock velocity exceeds a critical value. Amore recently suggested closure theory based on the maximum entropy principle yields symmetric hyperbolic moment equations. However, if moments higher than second order are included, the computational demand of this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments including the equilibrium state.Motivated by recent promising results of closed-form, singular closures based on the maximum entropy approach, we study regularized singular closures that become singular on a subset of moments when the regularizing terms are removed. In order to study some implications of singular closures, we use a recently proposed explicit closure for the 5-moment equations. We show that this closure theory results in a hyperbolic system that can mitigate the problem of sub-shocks independent of the shock wave velocity and handle strongly non-equilibrium gas flows.

scholarly journals Fundamental solutions to moment equations for the simulation of microscale gas flows

2016 ◽  
Vol 806 ◽  
pp. 413-436 ◽  
Author(s):  
D. A. Lockerby ◽  
B. Collyer
Keyword(s):  
Steady State ◽  
Gas Flow ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Gas Flows ◽  
Moment Equations ◽  
Linear Superposition ◽  
Mesh Free ◽  
External Flows ◽  
Non Equilibrium

Fundamental solutions (Green’s functions) to Grad’s steady-state linearised 13-moment equations for non-equilibrium gas flows are derived. The creeping microscale gas flows, to which they pertain, are important to understanding the behaviour of atmospheric particulate and the performance of many potential micro/nano technologies. Fundamental solutions are also derived for the regularised form of the steady-state linearised 13-moment equations, due to Struchtrup & Torrilhon (Phys. Fluids, vol. 15 (9), 2003, pp. 2668–2680). The solutions are compared to their classical and ubiquitous counterpart: the Stokeslet. For an illustration of their utility, the fundamental solutions to Grad’s equations are implemented in a linear superposition approach to modelling external flows. Such schemes are mesh free, and benefit from not having to truncate and discretise an infinite three-dimensional domain. The high accuracy of the technique is demonstrated for creeping non-equilibrium gas flow around a sphere, for which an analytical solution exists for comparison. Finally, to demonstrate the method’s geometrical flexibility, the flow generated between adjacent spheres held at a fixed uniform temperature difference is explored.

Non-Equilibrium Reacting Gas Flows

2009 ◽  
Author(s):  
Ekaterina Nagnibeda ◽  
Elena Kustova
Keyword(s):  
Gas Flows ◽  
Non Equilibrium

scholarly journals Atmospheric-pressure Non-equilibrium Microplasmas using Liquids and Miniature Gas Flows

2010 ◽  
Vol 130 (10) ◽  
pp. 899-906 ◽  
Author(s):  
Shozo Ishii ◽  
Naoki Shirai ◽  
Shinji Ibuka ◽  
Makoto Kanemaru ◽  
Jun Kikuchi
Keyword(s):  
Atmospheric Pressure ◽  
Gas Flows ◽  
Non Equilibrium
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