Conditional hyperbolic quadrature method of moments for kinetic equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:365

Article

Fox, Rodney O.^1,2,3,4  Laurent, Frederique^2,3  Vie, Aymeric^2,3 

[1] Iowa State Univ, Dept Chem & Biol Engn, 618 Bissell Rd, Ames, IA 50011 USA

[2] Univ Paris Saclay, CNRS, CentraleSupelec, Lab EM2C, 3 Rue Joliot Curie, F-91192 Gif Sur Yvette, France

[3] CentraleSupelec, Federat Math, FR CNRS 3487, 3 Rue Joliot Curie, F-91192 Gif Sur Yvette, France

[4] Iowa State Univ, Ctr Multiphase Flow Res & Educ, 2519 Union Dr, Ames, IA 50011 USA

关键词: Kinetic equation;    Quadrature-based moment methods;    Conditional quadrature method of moments;    Hyperbolic moment closures;   

DOI  :  10.1016/j.jcp.2018.03.025

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free