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.
翻译:本文介绍了基于子元素的休克捕捉不连续的 Galerkin (DG) 近似值的新战略。 设想是将DG 元素解释为数据收集, 并构建该数据集的低至高分化等级, 包括直至全顺序 DG 计划的第一个顺序定量量量方案。 不同的DG 离异性方案随后根据分元素多疑的单元格指标混合, 从而导致最终的离异化, 在单个的DG 元素中从低顺序到高顺序进行适应性混合。 目标是尽可能保持最高顺序的准确性, 即使在Sedov 测试中显示的极强冲击模拟中也是如此。 框架保留了标准DG 计划的位置, 因此非常适合与适应性中观改进和平行计算相结合。 数字测试显示了新休克捕法的子元素适应性适应行为及其高度准确性。