论文标题
光谱差和通量重建方案之间的准确性，稳定性和性能比较
Accuracy, Stability, and Performance Comparison between the Spectral Difference and Flux Reconstruction Schemes
论文作者
论文摘要
我们报告了不连续的光谱元件流量求解器的开发，该元素流量求解器包括光谱差和通量重建公式的实现。通过这个高阶框架，我们建立了一个基础，以在准确性，稳定性和性能方面对这两个方案进行公平准确的评估，并特别注意真实的光谱差异方案以及通过磁通重建公式恢复的修改光谱差异方案。在对光谱差异和通量重建方案的先前分析的基础上，我们提供了新型的非线性稳定性分析，对光谱差异方案。通过各种数值实验，我们证明了真实的基线光谱差异方案提供的额外稳定性，而无需显式过滤或脱氧化，因为其交错点的固有特征。这种布置导致对混叠错误的有利抑制，并改善了湍流较低的模拟所需的稳定性。
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation upon which to provide a fair and accurate assessment of these two schemes in terms of accuracy, stability, and performance with special attention to the true spectral difference scheme and the modified spectral difference scheme recovered via the flux reconstruction formulation. Building on previous analysis of the spectral difference and flux reconstruction schemes, we provide a novel nonlinear stability analysis of the spectral difference scheme. Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme without explicit filtering or de-aliasing due to its inherent feature of staggered flux points. This arrangement leads to favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows.
