论文标题
\ textit {a后验}在二维非结构性网格上，对高阶不连续的盖尔金方案的局部子校正校正
\textit{A Posteriori} local subcell correction of high-order discontinuous Galerkin scheme for conservation laws on two-dimensional unstructured grids
论文作者
论文摘要
我们介绍了[52]中引入的不连续的盖尔金（DG）方案的A后部局部子细胞校正的二维非结构化网格扩展。该技术是基于DG方案的重新制定作为有限体积（FV）的方法，例如方法，通过定义一些特定的数值通量，称为重建的通量。高阶DG数值方案与这种新的局部子电池校正技术相结合，可确保溶液的积极保存以及低振荡和尖锐的冲击表示。这种校正程序的主要思想是尽可能保留DG方案的高精度和非常精确的子电池分辨率，同时确保数值方法的鲁棒性和稳定性，并保留解决方案的物理可接受性。因此，A后验校正只能在需要的子单元尺度上局部应用，但仍确保局部方案保护。实际上，在每个时间步骤中，我们都会计算一个DG候选解决方案，并检查该解决方案是否可接受（例如，正，非振荡等）。将提出有关各种类型问题和测试用例的数值结果，以评估设计校正算法的良好性能。
We present the two-dimensional unstructured grids extension of the a posteriori local subcell correction of discontinuous Galerkin (DG) schemes introduced in [52]. The technique is based on the reformulation of DG scheme as a finite volume (FV) like method through the definition of some specific numerical fluxes referred to as reconstructed fluxes. High-order DG numerical scheme combined with this new local subcell correction technique ensures positivity preservation of the solution, along with a low oscillatory and sharp shocks representation. The main idea of this correction procedure is to retain as much as possible the high accuracy and the very precise subcell resolution of DG schemes, while ensuring the robustness and stability of the numerical method, as well as preserving physical admissibility of the solution. Consequently, an a posteriori correction will only be applied locally at the subcell scale where it is needed, but still ensuring the local scheme conservation. Practically, at each time step, we compute a DG candidate solution and check if this solution is admissible (for instance positive, non-oscillating, etc). Numerical results on various type problems and test cases will be presented to assess the very good performance of the design correction algorithm.
