CHyQMOM
swMATH ID:  34770 
Software Authors:  Fox, Rodney O.; Laurent, Frédérique; Vié, Aymeric 
Description:  Conditional hyperbolic quadrature method of moments for kinetic equations. The conditional quadrature method of moments (CQMOM) was introduced by Yuan and Fox (2011) [4] to reconstruct a velocity distribution function (VDF) from a finite set of its integer moments. The reconstructed VDF takes the form of a sum of weighted Dirac delta functions in velocity phase space, and provides a closure for the spatial flux term in the corresponding kinetic equation. The CQMOM closure for the flux leads to a weakly hyperbolic system of moment equations. In subsequent work by Chalons et al. (2010) [8], the Dirac delta functions were replaced by Gaussian distributions, which make the moment system hyperbolic but at the added cost of dealing with continuous distributions. Here, a hyperbolic version of CQMOM is proposed that uses weighted Dirac delta functions. While the moment set employed for multiGaussian and conditional HyQMOM (CHyQMOM) are equivalent, the latter is able to access all of moment space whereas the former cannot (e.g. arbitrary values of the fourthorder velocity moment in 1D phase space with two nodes). By making use of the properties of CHyQMOM in 2D phase space, it is possible to control a symmetrical subset of the optimal moments from Fox (2009) [24]. Furthermore, the moment sets for 2D problems are smaller for CHyQMOM than in the original CQMOM thanks to a judicious choice of the velocity abscissas in phase space. 
Homepage:  https://www.sciencedirect.com/science/article/pii/S0021999118301852 
Keywords:  kinetic equation; quadraturebased moment methods; conditional quadrature method of moments; hyperbolic moment closures 
Related Software:  OPQ; OpenQBMM; Fluidity; MFC; Mathematica; QBMMlib; HEE1GODF 
Cited in:  7 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Conditional hyperbolic quadrature method of moments for kinetic equations. Zbl 1395.82232 Fox, Rodney O.; Laurent, Frédérique; Vié, Aymeric 
2018

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top 5
Cited by 9 Authors
3  Fox, Rodney O. 
3  Laurent, Frédérique 
1  Böhmer, Niclas 
1  Cai, Zhenning 
1  Laboureur, Delphine 
1  Torrilhon, Manuel 
1  Van Cappellen, Maxim 
1  Vetrano, Maria Rosaria 
1  Vié, Aymeric 
Cited in 4 Serials
4  Journal of Computational Physics 
1  Journal of Fluid Mechanics 
1  SIAM Journal on Applied Mathematics 
1  Comptes Rendus. Mathématique. Académie des Sciences, Paris 
Cited in 4 Fields
6  Fluid mechanics (76XX) 
5  Statistical mechanics, structure of matter (82XX) 
2  Partial differential equations (35XX) 
1  Numerical analysis (65XX) 