Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations
Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations
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DOI：
10.1007/s10409-013-0042-1
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发表时间：
2013-07
影响因子：
3.5
通讯作者：
Zhen-hua Jiang;Chao Yan;Jian Yu
中科院分区：
文献类型：
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作者：
Zhen-hua Jiang;Chao Yan;Jian Yu
本文改进了三角形网格上求解可压缩Navier-Stokes方程的两种高阶间断Galerkin（DG）隐式算法。一个块上下对称高斯-赛德尔（BLU-SGS）方法实现为一个非线性迭代计划。提出了一种改进的LU-SGS方法（LLU-SGS），在保持原LU-SGS方法良好收敛性能的同时，减少了对内存的需求。这两种隐式格式都具有只存储对角块矩阵的显著优点。由此产生的隐式高阶DG方法，结合Hermite加权基本无振荡（HWENO）限制器，解决粘性流问题。数值结果表明，本文的隐式方法与显式方法相比，对于粘性激波流场的计算效率有了显著的提高，而HWENO限制器可以同时实现所需的无振荡激波转捩和设计的高阶精度。
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.