论文标题
不连续的Galerkin光谱元素方法的子限制策略
Subcell limiting strategies for discontinuous Galerkin spectral element methods
论文作者
论文摘要
我们提出了一个一般的子限制策略家族，以构建强大的高阶准确淋巴结不连续的Galerkin（DG）方案。主要策略是构建兼容的低阶有限体积（FV）类型离散化，以允许与高阶变体融合，以保证其他属性，例如物理量的界限和/或保证的熵耗散。 For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre-Gauss-Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex混合因素可以基于启发式障碍细胞指标，也可以使用磁通校正的传输方法中的想法。 通过仔细设计子电池FV方法的度量术语，可以将所得的方法用于非结构化的曲线网格，在局部保守，可以有效处理强震动，同时直接保证诸如密度，压力或熵等数量的物理界限。我们进一步表明，可以选择四种成分来恢复现有方法，例如可证明的熵耗散子电池冲击方法或稀疏不变域保存方法。 我们测试了提出的策略的多功能性，并混合并匹配四种成分，以解决具有挑战性的模拟设置，例如KPP问题（具有非凸线通量功能的双曲线保护定律），湍流和高超音波EULER模拟，以及具有冲击和湍流的MHD问题。
We present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre-Gauss-Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.
