scholarly journals Globally hyperbolic moment system by generalized Hermite expansion

2015 ◽  
Vol 45 (10) ◽  
pp. 1635-1676 ◽  
Author(s):  
YuWei FAN ◽  
Ruo LI
Keyword(s):  
Hermite Expansion ◽  
Globally Hyperbolic ◽  
Moment System

scholarly journals Globally Hyperbolic Regularization of Grad's Moment System

2013 ◽  
Vol 67 (3) ◽  
pp. 464-518 ◽  
Author(s):  
Zhenning Cai ◽  
Yuwei Fan ◽  
Ruo Li
Keyword(s):  
Globally Hyperbolic ◽  
Moment System

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.

Stability analysis of a class of globally hyperbolic moment system

2017 ◽  
Vol 15 (3) ◽  
pp. 609-633 ◽  
Author(s):  
Weifeng Zhao ◽  
Wen-An Yong ◽  
Li-Shi Luo
Keyword(s):  
Stability Analysis ◽  
Globally Hyperbolic ◽  
Moment System

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Grad's 13-moment system for a dense gas of inelastic spheres

1985 ◽  
Vol 87 (4) ◽  
pp. 355-377 ◽  
Author(s):  
J. T. Jenkins ◽  
M. W. Richman
Keyword(s):  
Dense Gas ◽  
Moment System

Defect of the five-thirds law using the Wiener-Hermite expansion

1989 ◽  
Vol 55 (5-6) ◽  
pp. 1089-1107 ◽  
Author(s):  
Tung -chen Chung ◽  
William C. Meecham
Keyword(s):  
Hermite Expansion
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