论文标题
具有后验限制的光谱差异方法：在一个和两个空间维度中应用于Euler方程
Spectral Difference method with a posteriori limiting: Application to the Euler equations in one and two space dimensions
论文作者
论文摘要
我们提出了一种新的数值方案，该方案将光谱差（SD）方法与\ emph {a-posteriori}一起使用经典Muscl-Hancock方案作为后备方案限制。它在流动的流动区域中提供了非常准确的解决方案，同时捕获了无虚假振荡的尖锐不连续性。我们利用基于SD控制量的SD方案与有限体积（FV）方案之间的严格等价性，以实现直接的限制策略。在高阶时间整合ADER方案的每个阶段结束时，我们在许多数值和物理标准下检查高阶解决方案是否可以接受。如果没有，我们会用强大的二阶MUSCL后备方案中的通量代替陷入困境的单元的高阶通量。我们将我们的方法应用于1D和2D Euler方程的一系列测试问题。我们证明，SD和ADER的这种组合几乎提供了数量任意的高度准确性，同时保留了良好的子元素冲击捕获功能。
We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using the classical MUSCL-Hancock scheme as fallback scheme. It delivers very accurate solutions in smooth regions of the flow, while capturing sharp discontinuities without spurious oscillations. We exploit the strict equivalence between the SD scheme and a Finite-Volume (FV) scheme based on the SD control volumes to enable a straightforward limiting strategy. At the end of each stage of our high-order time-integration ADER scheme, we check if the high-order solution is admissible under a number of numerical and physical criteria. If not, we replace the high-order fluxes of the troubled cells by fluxes from our robust second-order MUSCL fallback scheme. We apply our method to a suite of test problems for the 1D and 2D Euler equations. We demonstrate that this combination of SD and ADER provides a virtually arbitrary high order of accuracy, while at the same time preserving good sub-element shock capturing capabilities.
