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A high-order moment limiter for the discontinuous Galerkin method on triangular meshes
Journal of Computational Physics ( IF 4.1 ) Pub Date : 2021-02-10 , DOI: 10.1016/j.jcp.2021.110188
Krishna Dutt , Lilia Krivodonova

We propose a moment limiter of arbitrary high order for the discontinuous Galerkin method on unstructured triangular meshes. The limiter works by hierarchically limiting solution coefficients (moments) by comparing them to reconstructed directional derivatives along specific directions. Limiting along these directions is performed using one-dimensional minmod slope limiters. The stencil used to reconstruct directional derivatives consists of only eight mesh elements and can be computed in the pre-processing stage. Due to a low number of operations involved in limiting, the limiter takes only a fraction of the total computing time for the modal discontinuous Galerkin method. We present numerical examples showing that limited solutions retain the theoretical rate of convergence and are robust in the presence of discontinuities.



中文翻译:

三角网格上不连续Galerkin方法的高阶矩限制器

对于非结构三角形网格上的不连续Galerkin方法,我们提出了任意高阶矩限制器。限幅器通过将解系数(矩)与沿特定方向的重构方向导数进行比较来分层限制解系数(矩)来工作。使用一维minmod斜率限制器执行沿这些方向的限制。用于重建方向导数的模具仅由八个网格元素组成,可以在预处理阶段进行计算。由于限制所涉及的操作数量少,对于模态不连续伽勒金方法,限制器仅占用总计算时间的一小部分。我们提供的数值示例表明,有限的解保留了理论上的收敛速度,并且在存在不连续性的情况下很健壮。

更新日期:2021-02-12
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