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 multi-Gaussian 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 fourth-order velocity moment in 1-D phase space with two nodes). By making use of the properties of CHyQMOM in 2-D phase space, it is possible to control a symmetrical subset of the optimal moments from Fox (2009) [24]. Furthermore, the moment sets for 2-D 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; quadrature-based moment methods; conditional quadrature method of moments; hyperbolic moment closures
Related Software: OPQ; OpenQBMM; Fluidity; MFC; Mathematica; QBMMlib; HE-E1GODF
Cited in: 7 Publications

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