Stability evaluation of high-order splitting method for incompressible flow based on discontinuous velocity and continuous pressure
Stability evaluation of high-order splitting method for incompressible flow based on discontinuous velocity and continuous pressure
复制标题
基于不连续速度和连续压力的不可压缩流高阶分裂方法稳定性评估
DOI：
10.1177/1687814019855586
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发表时间：
2019
影响因子：
2.1
通讯作者：
Xuejun Yang
中科院分区：
文献类型：
--
作者：
Liyang Xu;Xinhai Xu;Xiaoguang Ren;Yunrui Guo;Yongquan Feng;Xuejun Yang
在这项工作中，我们处理不可压缩流动的基于间断Galerkin离散速度和标准连续近似压力的速度修正格式的高阶求解器。最近，关于纯间断Galerkin方法的小时间步长不稳定性已有报道，其中速度和压力都是用间断Galerkin离散的。在混合间断Galerkin-连续Galerkin方法的背景下考察这些不稳定性是很有趣的。通过数值研究，我们发现间断Galerkin-连续Galerkin方法在相同的位形下表现出很大的稳定性。一致的速度散度离散格式有助于在较小的时间步长下获得更准确的结果。由于等阶间断Galerkin-连续Galerkin方法不满足inf-sup稳定性要求，研究了高雷诺数流动的不稳定性。数值结果表明，要获得一个稳健的系统，需要高的网格分辨率和高的多项式阶数。利用这些结论，间断Galerkin-连续Galerkin方法能够获得高阶空间收敛速度，并能精确地模拟高雷诺数流动。通过一系列经典的基准问题对该算法进行了测试，并与纯间断Galerkin格式进行了比较，证明了算法的有效性。
In this work, we deal with high-order solver for incompressible flow based on velocity correction scheme with discontinuous Galerkin discretized velocity and standard continuous approximated pressure. Recently, small time step instabilities have been reported for pure discontinuous Galerkin method, in which both velocity and pressure are discretized by discontinuous Galerkin. It is interesting to examine these instabilities in the context of mixed discontinuous Galerkin–continuous Galerkin method. By means of numerical investigation, we find that the discontinuous Galerkin–continuous Galerkin method shows great stability at the same configuration. The consistent velocity divergence discretization scheme helps to achieve more accurate results at small time step size. Since the equal order discontinuous Galerkin–continuous Galerkin method does not satisfy inf-sup stability requirement, the instability for high Reynolds number flow is investigated. We numerically demonstrate that fine mesh resolution and high polynomial order are required to obtain a robust system. With these conclusions, discontinuous Galerkin–continuous Galerkin method is able to achieve high-order spatial convergence rate and accurately simulate high Reynolds flow. The solver is tested through a series of classical benchmark problems, and efficiency improvement is proved against pure discontinuous Galerkin scheme.