论文标题
不连续的Galerkin方法的子元素自适应冲击捕获方法
A Sub-Element Adaptive Shock Capturing Approach for Discontinuous Galerkin Methods
论文作者
论文摘要
在本文中，提出了一种基于子元素的电击捕获不连续的盖尔金（DG）近似值的新策略。这个想法是将DG元素解释为数据集合，并在这组数据上构建一个低至高阶离散化的层次结构，包括到完整的DG方案的一阶有限体积方案。然后，根据子元素障碍细胞指示器将不同的DG离散化融合在一起，导致最终离散化，该离散化在单个DG元素中从低阶到高阶的自适应融合。目的是保持尽可能多的高阶准确度，即使在具有非常强烈的冲击的模拟中，如在Sedov测试中提出。该框架保留了标准DG方案的局部性，因此非常适合与自适应网格的细化和并行计算结合使用。数值测试证明了新的冲击捕获方法的子元素自适应行为及其高精度。
In this paper, a new strategy for a sub-element based shock capturing for discontinuous Galerkin (DG) approximations is presented. The idea is to interpret a DG element as a collection of data and construct a hierarchy of low to high order discretizations on this set of data, including a first order finite volume scheme up to the full order DG scheme. The different DG discretizations are then blended according to sub-element troubled cell indicators, resulting in a final discretization that adaptively blends from low to high order within a single DG element. The goal is to retain as much high order accuracy as possible, even in simulations with very strong shocks, as e.g. presented in the Sedov test. The framework retains the locality of the standard DG scheme and is hence well suited for a combination with adaptive mesh refinement and parallel computing. The numerical tests demonstrate the sub-element adaptive behavior of the new shock capturing approach and its high accuracy.
