A stochastic asymptotic-preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty

JOURNAL OF COMPUTATIONAL PHYSICS

卷:335

Article

Jin, Shi^1,2,3  Shu, Ruiwen¹ 

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Shanghai Jiao Tong Univ, MOELSEC, Sch Math Sci, Inst Nat Sci, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, SHL MAC, Shanghai 200240, Peoples R China

关键词: Kinetic-fluid model;    Disperse particles;    Uncertain quantification;    Asymptotic-preserving;    Projection method;    Stochastic Galerkin;   

DOI  :  10.1016/j.jcp.2017.01.059

来源: Elsevier

【 摘 要 】

In this paper we consider a kinetic-fluid model for disperse two-phase flows with uncertainty. We propose a stochastic asymptotic-preserving (s-AP) scheme in the generalized polynomial chaos stochastic Galerkin (gPC-sG) framework, which allows the efficient computation of the problem in both kinetic and hydrodynamic regimes. The s-AP property is proved by deriving the equilibrium of the gPC version of the Fokker-Planck operator. The coefficient matrices that arise in a Helmholtz equation and a Poisson equation, essential ingredients of the algorithms, are proved to be positive definite under reasonable and mild assumptions. The computation of the gPC version of a translation operator that arises in the inversion of the Fokker-Planck operator is accelerated by a spectrally accurate splitting method. Numerical examples illustrate the s-AP property and the efficiency of the gPC-sG method in various asymptotic regimes. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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