论文标题
高阶熵保存ADER方案
High order entropy preserving ADER scheme
论文作者
论文摘要
在本文中，我们开发了一个完全分散的熵保存ADER-DER-DISCONCONTINCLUES GALERKIN（ADER-DG）方法。为了获得此期望的结果，我们为该方法的空间部分配备了熵校正项，以平衡空间中的熵产生，灵感来自于Abgrall的工作。尽管对于时间限制，我们应用了凯奇森（Ketcheson）引入的放松方法，该方法允许修改时间步长以保留机器精度的熵。据我们所知，这是第一次构建可证明的完全离散的熵保存ADER-DG方案。我们通过各种数值模拟来验证我们的理论结果。
In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin (ADER-DG) method. To obtain this desired result, we equip the space part of the method with entropy correction terms that balance the entropy production in space, inspired by the work of Abgrall. Whereas for the time-discretization we apply the relaxation approach introduced by Ketcheson that allows to modify the timestep to preserve the entropy to machine precision. Up to our knowledge, it is the first time that a provable fully discrete entropy preserving ADER-DG scheme is constructed. We verify our theoretical results with various numerical simulations.
