On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes
On discretely entropy stable weight-adjusted discontinuous Galerkin methods: curvilinear meshes
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DOI：
10.1016/j.jcp.2018.11.010
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发表时间：
2019-02-01
影响因子：
4.1
通讯作者：
Wilcox, Lucas C.
中科院分区：
文献类型：
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作者：
Chan, Jesse;Wilcox, Lucas C.
在曲线网格上构造了非线性双曲型守恒律方程的熵守恒和熵稳定的间断Galerkin（DG）离散格式。由此产生的计划保持一个连续的全球熵不等式的半离散正交近似。证明需要满足离散几何守恒定律，我们通过适当的多项式近似来执行。我们扩展的熵保守和熵稳定DG计划的建设时，高阶曲线质量矩阵近似使用低存储的权重调整近似的情况下，并描述如何保持全局守恒性质下，这样的近似。对于某些类型的曲线网格，这些权重调整的近似提供了最佳的收敛速度。最后，通过三角形和四面体网格下可压缩Euler方程的数值实验，验证了欠分辨解的高阶精度、局部守恒性和离散熵守恒或耗散性. (C)2018爱思唯尔公司All rights reserved.
We construct entropy conservative and entropy stable discontinuous Galerkin (DG) discretizations for time-dependent nonlinear hyperbolic conservation laws on curvilinear meshes. The resulting schemes preserve a semi-discrete quadrature approximation of a continuous global entropy inequality. The proof requires the satisfaction of a discrete geometric conservation law, which we enforce through an appropriate polynomial approximation. We extend the construction of entropy conservative and entropy stable DG schemes to the case when high order curvilinear mass matrices are approximated using low-storage weight-adjusted approximations, and describe how to retain global conservation properties under such an approximation. For certain types of curvilinear meshes, these weight-adjusted approximations deliver optimal rates of convergence. Finally, the high order accuracy, local conservation, and discrete conservation or dissipation of entropy for under-resolved solutions are verified through numerical experiments for the compressible Euler equations on triangular and tetrahedral meshes. (C) 2018 Elsevier Inc. All rights reserved.