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Mathematical Problems in Engineering - Volume 2015 2015, Article ID 940257, 11 pages -

Research Article

Department of Applied Mathematics, Xidian University, Xi’an 710071, China

Department of Applied Mathematics, Xianyang Normal University, Xianyang 712000, China

School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China

Received 23 June 2014; Revised 31 August 2014; Accepted 31 August 2014

Academic Editor: Shaofan Li

Copyright © 2015 Xinrong Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Efficient implicit predictor-corrector LU-SGS discontinuous Galerkin DG approach for compressible Euler equations on unstructured grids is investigated by adding the error compensation of high-order term. The original LU-SGS and GMRES schemes for DG method are discussed. Van Albada limiter is employed to make the scheme monotone. The numerical experiments performed for the transonic inviscid flows around NACA0012 airfoil, RAE2822 airfoil, and ONERA M6 wing indicate that the present algorithm has the advantages of low storage requirements and high convergence acceleration. The computational efficiency is close to that of GMRES scheme, nearly 2.1 times greater than that of LU-SGS scheme on unstructured grids for 2D cases, and almost 5.5 times greater than that of RK4 on unstructured grids for 3D cases.

Autor: Xinrong Ma, Sanyang Liu, and Gongnan Xie



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