A Comprehensive Comparison of Higher-Order Moment Equations and DSMC for Force-Driven Poiseuille Gas Flow

2011 ◽  
Author(s):  
R. S. Myong ◽  
J. H. Park
Keyword(s):  
Gas Flow ◽  
Higher Order ◽  
Order Moment ◽  
Moment Equations ◽  
Comprehensive Comparison

scholarly journals A Hierarchy of Diffusive Higher-Order Moment Equations for Semiconductors

2007 ◽  
Vol 68 (1) ◽  
pp. 171-198 ◽  
Author(s):  
Ansgar Jüngel ◽  
Stefan Krause ◽  
Paola Pietra
Keyword(s):  
Higher Order ◽  
Order Moment ◽  
Moment Equations

scholarly journals Higher-order moment theories for dilute granular gases of smooth hard spheres

2017 ◽  
Vol 836 ◽  
pp. 451-501 ◽  
Author(s):  
Vinay Kumar Gupta ◽  
Priyanka Shukla ◽  
Manuel Torrilhon
Keyword(s):  
Coefficient Of Restitution ◽  
Higher Order ◽  
Order Moment ◽  
Granular Gases ◽  
Moment Equations ◽  
Moment Theory ◽  
Moment System ◽  
The Stability ◽  
Homogeneous Cooling State ◽  
Critical Wavenumber

Grad’s method of moments is employed to develop higher-order Grad moment equations – up to the first 26 moments – for dilute granular gases within the framework of the (inelastic) Boltzmann equation. The homogeneous cooling state of a freely cooling granular gas is investigated with the Grad 26-moment equations in a semi-linearized setting and it is shown that the granular temperature in the homogeneous cooling state still decays according to Haff’s law while the other higher-order moments decay on a faster time scale. The nonlinear terms of the fully contracted fourth moment are also considered and, by exploiting the stability analysis of fixed points, it is shown that these nonlinear terms have a negligible effect on Haff’s law. Furthermore, an even larger Grad moment system, which includes the fully contracted sixth moment, is also scrutinized and the stability analysis of fixed points is again exploited to conclude that even the inclusion of the scalar sixth-order moment into the Grad moment system has a negligible effect on Haff’s law. The constitutive relations for the stress and heat flux (i.e. the Navier–Stokes and Fourier relations) are derived through the Grad 26-moment equations and compared with those obtained via the Chapman–Enskog expansion and via computer simulations. The linear stability of the homogeneous cooling state is analysed through the Grad 26-moment system and various subsystems by decomposing them into longitudinal and transverse systems. It is found that one eigenmode in both longitudinal and transverse systems in the case of inelastic gases is unstable. By comparing the eigenmodes from various theories, it is established that the 13-moment eigenmode theory predicts that the unstable heat mode of the longitudinal system remains unstable for all wavenumbers below a certain coefficient of restitution, while any other higher-order moment theory shows that this mode becomes stable above some critical wavenumber for all values of the coefficient of restitution. In particular, the Grad 26-moment theory leads to a smooth profile for the critical wavenumber, in contrast to the other considered theories. Furthermore, the critical system size obtained through the Grad 26-moment theory is in excellent agreement with that obtained through existing theories.

Heat and Mass Transfer of a Rarefied Gas in a Driven Micro-Cavity

2009 ◽  
Author(s):  
X. J. Gu ◽  
B. John ◽  
G. H. Tang ◽  
D. R. Emerson
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Transport Model ◽  
Direct Simulation Monte Carlo ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Order Moment ◽  
Moment Equations ◽  
Micro Cavity ◽  
Non Equilibrium

A high-order moment method is employed to construct the transport model for non-equilibrium gas flow in micro-scale geometries. The motion of a gas in a two-dimensional square micro-cavity is solved using the 26 moment equations for low Reynolds and Mach number flows in the early transition regime. The computed velocity and temperature fields are compared with data obtained from the direct simulation Monte Carlo method. It is found that the 26 moment equations are able to capture the non-equilibrium phenomena in a driven micro-cavity, such as counter-gradient heat transfer, which are not embedded in the Navier-Stokes-Fourier equations.

scholarly journals Comparing Entropies in Portfolio Diversification with Fuzzy Value at Risk and Higher-Order Moment

2020 ◽  
pp. 1-16
Author(s):  
Mahdi Pourrafiee ◽  
AmirHossein Nafei ◽  
Shokoufe Banihashemi ◽  
S. Pourmohammad Azizi
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Higher Order ◽  
Portfolio Diversification ◽  
Order Moment
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