A hierarchical uniformly high order DG-IMEX scheme for the 1D BGK equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:336

Article

Xiong, Tao^1,3  Qiu, Jing-Mei² 

[1] Xiamen Univ, Sch Math Sci, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Fujian, Peoples R China

[2] Univ Houston, Dept Math, Houston, TX 77004 USA

[3] Univ Toulouse III, Inst Math Toulouse, UMR 5219, 118 Route Narbonne, F-31062 Toulouse, France

关键词: A hierarchical scheme;    Compressible Euler equations;    Compressible Navier-Stokes equations;    Asymptotic Preserving;    Nodal Discontinuous Galerkin;    High order;    IMEX;    BGK equation;   

DOI  :  10.1016/j.jcp.2017.01.032

来源: Elsevier

【 摘 要 】

A class of high order nodal discontinuous Galerkin implicit-explicit (DG-IMEX) schemes with asymptotic preserving (AP) property has been developed for the one-dimensional (ID) BGK equation in Xiong et al. (2015) [40], based on a micro-macro reformulation. The schemes are globally stiffly accurate and asymptotically consistent, and as the Knudsen number becomes small or goes to zero, they recover first the compressible Navier-Stokes (CNS) and then the Euler limit. Motivated by the recent work of Filbet and Rey (2015) [27] and the references therein, in this paper, we propose a hierarchical high order AP method, namely kinetic, CNS and Euler solvers are automatically applied in regions where their corresponding models are appropriate. The numerical solvers for different regimes are coupled naturally by interface conditions. To the best of our knowledge, the resulting scheme is the very first hierarchical one being proposed in the literature, that enjoys AP property as well as uniform high order accuracy. Numerical experiments demonstrate the efficiency and effectiveness of the proposed approach. As time evolves, three different regimes are dynamically identified and naturally coupled, leading to significant CPU time savings (more than 80% for some of our test problems). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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