De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods
De-Aliasing Through Over-Integration Applied to the Flux Reconstruction and Discontinuous Galerkin Methods
复制标题
通过过积分去混叠应用于通量重建和不连续伽辽金方法
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
J. Debonis
中科院分区：
文献类型：
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作者：
S. Spiegel;H. Huynh;J. Debonis
随着计算机处理能力的提高，高阶方法在湍流计算中迅速流行起来。通量重建（FR）方法为包括间断Galerkin（DG）、谱差分（SD）和谱体积（SV）在内的广泛的一类高阶方法提供了一个统一的框架。它提供了一种简单、有效和容易的方法来实现通过控制方程的微分形式导出的基于代数的方法。虽然高阶方法最近取得了成功，但已知它们在应用于欠分辨非线性问题时会由于多项式混叠而引入数值不稳定性。混叠错误已被广泛研究，参考DG方法，但是，他们的研究有关FR方法主要限于选择的节点内使用的每个细胞。在这里，我们扩展了一些用于DG方法的去混叠技术，主要是过积分，FR框架。我们的研究结果表明，过度整合消除混叠错误，但可能无法消除所有的不稳定性所造成的分辨率不足（FR以及DG）。
High-order methods are quickly becoming popular for turbulent flows as the amount of computer processing power increases. The flux reconstruction (FR) method presents a unifying framework for a wide class of high-order methods including discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV). It offers a simple, efficient, and easy way to implement nodal-based methods that are derived via the differential form of the governing equations. Whereas high-order methods have enjoyed recent success, they have been known to introduce numerical instabilities due to polynomial aliasing when applied to under-resolved nonlinear problems. Aliasing errors have been extensively studied in reference to DG methods; however, their study regarding FR methods has mostly been limited to the selection of the nodal points used within each cell. Here, we extend some of the de-aliasing techniques used for DG methods, primarily over-integration, to the FR framework. Our results show that over-integration does remove aliasing errors but may not remove all instabilities caused by insufficient resolution (for FR as well as DG).
影响因子：
3.4
作者：
Gassner, Gregor J.;Beck, Andrea D.
通讯作者：
Beck, Andrea D.