p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
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DOI：
10.1016/j.jcp.2005.01.005
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发表时间：
2005-07
影响因子：
4.1
通讯作者：
K. Fidkowski;Todd A. Oliver;James Lu;D. Darmofal
中科院分区：
文献类型：
--
作者：
K. Fidkowski;Todd A. Oliver;James Lu;D. Darmofal
给出了可压缩Navier-Stokes方程的高阶不连续Galerkin有限元离散化的p-多重网格解算法。该算法采用一种元素线雅可比平滑法，其中基于标量对流扩散方程的p=0离散化，通过耦合形成元素线。对流扩散的两级p-多重网格算法的傅里叶分析表明，单元线Jacobi比单元Jacobi有显著的改进，特别是对于高雷诺数流动和拉伸网格。非粘性和粘性测试用例的结果表明，最佳的hp+1阶精度以及与p无关的多网格收敛率，至少达到p=3。此外，对于考虑的光滑问题，在达到所需的高精度水平所需的时间方面，p-细化优于h-细化。
We present a p-multigrid solution algorithm for a high-order discontinuous Galerkin finite element discretization of the compressible Navier–Stokes equations. The algorithm employs an element line Jacobi smoother in which lines of elements are formed using coupling based on a p=0 discretization of the scalar convection–diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection–diffusion shows that element line Jacobi presents a significant improvement over element Jacobi especially for high Reynolds number flows and stretched grids. Results from inviscid and viscous test cases demonstrate optimal hp+1order of accuracy as well as p-independent multigrid convergence rates, at least up to p=3. In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.