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

作　　者：Zhen-Hua Jiang Chao Yan Jian Yu 

机构地区：[1]College of Aeronautics Science and Engineering, Beijing University of Aeronautics and Astronautics

出　　处：《Acta Mechanica Sinica》2013年第4期526-533,共8页力学学报（英文版）

基　　金：supported by the National Basic Research Program of China(2009CB724104)

摘　　要：Two types of implicit algorithms have been im- proved for high order discontinuous Galerkin （DG） method to solve compressible Navier-Stokes （NS） equations on tri- angular grids. A block lower-upper symmetric Gauss- Seidel （BLU-SGS） approach is implemented as a nonlin- ear 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 origi- nal LU-SGS approach. Both implicit schemes have the sig- nificant 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 tran- sition and the designed high-order accuracy simultaneously.Two types of implicit algorithms have been im- proved for high order discontinuous Galerkin （DG） method to solve compressible Navier-Stokes （NS） equations on tri- angular grids. A block lower-upper symmetric Gauss- Seidel （BLU-SGS） approach is implemented as a nonlin- ear 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 origi- nal LU-SGS approach. Both implicit schemes have the sig- nificant 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 tran- sition and the designed high-order accuracy simultaneously.

关 键 词：Discontinuous Galerkin （DG） scheme ~ Implicitmethod ~ HWENO ~ High order ~ Unstructured grids 

分 类 号：O357[理学—流体力学]