Runge-Kutta central discontinuous Galerkin BGK method for the Navier-Stokes equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Ren, Tan¹  Hu, Jun¹  Xiong, Tao²  Qiu, Jing-Mei² 

[1] Beijing Inst Technol, Sch Aerosp Engn, Beijing 100081, Peoples R China

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

关键词: Central discontinuous Galerkin method;    Gas-kinetic scheme;    BGK model;    Navier-Stokes equations;    Computational fluid dynamics;   

DOI  :  10.1016/j.jcp.2014.06.045

来源: Elsevier

【 摘 要 】

In this paper, we propose a Runge-Kutta (RK) central discontinuous Galerkin (CDG) gas-kinetic BGK method for the Navier-Stokes equations. The proposed method is based on the CDG method defined on two sets of overlapping meshes to avoid discontinuous solutions at cell interfaces, as well as the gas-kinetic BGK model to evaluate fluxes for both convection and diffusion terms. Redundant representation of the numerical solution in the CDG method offers great convenience in the design of gas-kinetic BGK fluxes. Specifically, the evaluation of fluxes at cell interfaces of one set of computational mesh is right inside the cells of the staggered mesh, hence the corresponding particle distribution function for flux evaluation is much simpler than that in existing gas-kinetic BGK methods. As a central scheme, the proposed CDG-BGK has doubled the memory requirement as the corresponding DG scheme; on the other hand, for the convection part, the CFL time step constraint of the CDG method for numerical stability is relatively large compared with that for the DG method. Numerical boundary conditions have to be treated with special care. Numerical examples for 1D and 2D viscous flow simulations are presented to validate the accuracy and robustness of the proposed RK CDG-BGK method. (C) 2014 Elsevier Inc. All rights reserved.

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