Discretely entropy stable weight-adjusted discontinuous Galerkin methods on curvilinear meshes
Discretely entropy stable weight-adjusted discontinuous Galerkin methods on curvilinear meshes
复制标题
曲线网格上的离散熵稳定权重调整间断伽辽金方法
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
L. Wilcox
中科院分区：
文献类型：
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作者：
Jesse Chan;L. Wilcox
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高精度间断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。我们将熵保守和熵稳定DG格式的构造扩展到使用低存储权重调整近似来近似高阶精确曲线质量矩阵的情况，并描述了如何在这样的近似下保持全局保守性。在三角形和四面体网格上对可压缩欧拉方程进行了数值实验，验证了理论结果。
We construct entropy conservative and entropy stable high order accurate 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 accurate curvilinear mass matrices are approximated using low-storage weight-adjusted approximations, and describe how to retain global conservation properties under such an approximation. The theoretical results are verified through numerical experiments for the compressible Euler equations on triangular and tetrahedral meshes.
影响因子：
4.1
作者：
Chan, Jesse
通讯作者：
Chan, Jesse