论文标题
三角形上的一系列能量稳定通量重建方法
An extended range of energy stable flux reconstruction methods on triangles
论文作者
论文摘要
我们通过在二维中开发和应用逐个方的框架的开发和应用，在三角形上介绍了三角形上的稳定通量重建方法（FR）方法。然后，这种稳定方案的扩展范围被证明包含三角形上\ citet {castonguay2011}的单个参数方案，我们的定义使得为那些单个参数家族开发更广泛的稳定性界限。先前已经使用傅立叶分析发现了三角元素上的稳定的上环光谱差异（SD）方案。我们使用扩展的FR方案范围来研究三角形上SD方法的线性稳定性，发现在这组FR方法中可以恢复唯一的一阶SD方案。
We present an extended range of stable flux reconstruction (FR) methods on triangles through the development and application of the summation-by-parts framework in two-dimensions. This extended range of stable schemes is then shown to contain the single parameter schemes of \citet{Castonguay2011} on triangles, and our definition enables wider stability bounds to be developed for those single parameter families. Stable upwinded spectral difference (SD) schemes on triangular elements have previously been found using Fourier analysis. We used our extended range of FR schemes to investigate the linear stability of SD methods on triangles, and it was found that a only first order SD scheme could be recovered within this set of FR methods.
