论文标题
各种多项式基础的四边形上的稳定通量重建方案的扩展范围
An extended range of stable flux reconstruction schemes on quadrilaterals for various polynomial bases
论文作者
论文摘要
使用逐个组合方法开发的扩展范围的能量稳定通量重建方案在四组多项式碱基的四边形元素上介绍。对于最大顺序碱基，找到了一组新的校正功能，这些校正功能会导致稳定方案。但是，对于一系列订单，表明只能将单个校正函数施放为张量产品。随后，使用广义分析框架鉴定了校正功能，该框架导致四边形上的总顺序和近似欧几里得的多项式基础的稳定方案 - 以前在通量重建的背景下尚未探索过。结果表明，近似欧几里得的秩序基础可以提供与最大订单基础相似的数值准确性，但每个元素的点较少，因此成本较低。
An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements for various sets of polynomial bases. For the maximal order bases, a new set of correction functions which result in stable schemes is found. However, for a range of orders it is shown that only a single correction function can be cast as a tensor-product. Subsequently, correction functions are identified using a generalised analytic framework that results in stable schemes for total order and approximate Euclidean order polynomial bases on quadrilaterals -- which have not previously been explored in the context of flux reconstruction. It is shown that the approximate Euclidean order basis can provide similar numerical accuracy as the maximal order basis but with fewer points per element, and thus lower cost.
