论文标题
通过物理约束限制器，神经网络和多项式歼灭与高阶有限体积方案中的控制振荡进行比较
Comparison to control oscillations in high-order Finite Volume schemes via physical constraint limiters, neural networks and polynomial annihilation
论文作者
论文摘要
在过去的几十年中，建立高阶结构的数值方案来解决双曲保护法，并且存在着各种不同的Ansatzes。在本文中，我们比较了三种完全不同的方法，即物理约束限制，深度神经网络以及多项式歼灭在构建高阶振荡无限量（FV）混合方案中的应用。我们进一步分析了它们的分析和数值特性。我们证明所有技术都可以使用并产生高效的FV方法，但还带有一些其他缺点，我们指出。我们对不同混合策略的调查应导致对这些技术的更好理解，并可以转移到其他使用类似思想的数值方法中。
The construction of high-order structure-preserving numerical schemes to solve hyperbolic conservation laws has attracted a lot of attention in the last decades and various different ansatzes exist. In this paper, we compare three completely different approaches, i.e. physical constraint limiting, deep neural networks and the application of polynomial annihilation to construct high-order oscillation free Finite Volume (FV) blending schemes. We further analyze their analytical and numerical properties. We demonstrate that all techniques can be used and yield highly efficient FV methods but also come with some additional drawbacks which we point out. Our investigation of the different blending strategies should lead to a better understanding of those techniques and can be transferred to other numerical methods as well which use similar ideas.
