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Acta Mechanica Sinica

, Volume 29, Issue 4, pp 526–533 | Cite as

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

  • Zhen-Hua JiangEmail author
  • Chao Yan
  • Jian Yu
Research Paper

Abstract

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Keywords

Discontinuous Galerkin (DG) scheme Implicit method HWENO High order Unstructured grids 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of Aeronautics Science and EngineeringBeijing University of Aeronautics and AstronauticsBeijingChina

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