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首页> 外文期刊>Journal of Computational Physics >High-order multi-dimensional limiting strategy with subcell resolution I. Two-dimensional mixed meshes
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High-order multi-dimensional limiting strategy with subcell resolution I. Two-dimensional mixed meshes

机译：具有子单元分辨率的高阶多维限制策略I.二维混合网格

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The present paper deals with a new improvement of hierarchical multi-dimensional limiting process for resolving the subcell distribution of high-order methods on two-dimensional mixed meshes. From previous studies, the multi-dimensional limiting process (MLP) was hierarchically extended to the discontinuous Galerkin (DG) method and the flux reconstruction/correction procedure via reconstruction (FR/CPR) method on simplex meshes. It was reported that the hierarchical MLP (hMLP) shows several remarkable characteristics such as the preservation of the formal order-of-accuracy in smooth region and a sharp capturing of discontinuities in an efficient and accurate manner. At the same time, it was also surfaced that such characteristics are valid only on simplex meshes, and numerical Gibbs-Wilbraham oscillations are concealed in subcell distribution in the form of high-order polynomial modes. Subcell Gibbs-Wilbraham oscillations become potentially unstable near discontinuities and adversely affect numerical solutions in the sense of cell-averaged solutions as well as subcell distributions. In order to overcome the two issues, the behavior of the hMLP on mixed meshes is mathematically examined, and the simplex-decomposed Pl-projected MLP condition and smooth extrema detector are derived. Secondly, a troubled-boundary detector is designed by analyzing the behavior of computed solutions across boundary-edges. Finally, hMLP_BD is proposed by combining the simplex-decomposed Pl-projected MLP condition and smooth extrema detector with the troubled-boundary detector. Through extensive numerical tests, it is confirmed that the hMLP_BD scheme successfully eliminates subcell oscillations and provides reliable subcell distributions on two-dimensional triangular grids as well as mixed grids, while preserving the expected order-of-accuracy in smooth region. (C) 2018 Elsevier Inc. All rights reserved.
机译：本文涉及分层多维限制过程的新改进，用于解决二维混合网格上的高阶方法的子单元分布。根据以前的研究，通过在单纯形网格上的重建（FR / CPR）方法进行分层扩展到不连续的Galerkin（DG）方法和磁通重建/校正过程的多维限制过程（MLP）。据报道，等级MLP（HMLP）显示了几种显着的特征，例如在平滑区域中保存正式的准确度，并以有效和准确的方式急剧捕获不连续性。同时，它还浮出水面，即这种特性仅在单纯形网上有效，并且以高阶多项式模式的形式在子单元分布中隐藏数值GIBBS-WILBRAHAM振荡。子单元GIBBS-WILBRAHAM振荡在近不连续性潜在不稳定，并对细胞平均解决方案以及子单元分布的感觉产生不利影响数值解决方案。为了克服这两个问题，数学地检查了混合网格上的HMLP的行为，导出了单独的分解的PL投影MLP条件和平滑的极值检测器。其次，通过分析跨边界边缘的计算解决方案的行为来设计令人烦恼的边界检测器。最后，通过将Simplex分解的PL投影的MLP条件和具有困扰边界检测器的平滑极值检测器组合来提出HMLP_BD。通过广泛的数值测试，确认HMLP_BD方案成功消除了子电池振荡，并提供了在二维三角网格和混合网格上的可靠的子单元分布，同时保留平滑区域中的预期准确度。 （c）2018年Elsevier Inc.保留所有权利。

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