On the Order Reduction of Entropy Stable DGSEM for the Compressible Euler Equations
On the Order Reduction of Entropy Stable DGSEM for the Compressible Euler Equations
复制标题
可压缩欧拉方程熵稳定DGSEM的降阶
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
G. Gassner
中科院分区：
文献类型：
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作者：
F. Hindenlang;G. Gassner
当使用熵稳定的DGSEM-LGL变体时，收敛的实验阶数是否较低？近年来，关于熵稳定的Legendre-Gauss-Lobatto节点配置间断Galerkin谱元法（DGSEM）的收敛性问题出现了争论。虽然它是有据可查的熵保守的变体，没有额外的接口耗散时，测试其实验收敛阶显示出奇偶行为，在文献中的结果是不太清楚的DGSEM-LGL的熵稳定版本，其中明确的黎曼求解器类型的耗散添加在元素接口。我们有助于正在进行的讨论和目前的数值实验的可压缩欧拉方程，在那里我们调查的数值表面通量函数的选择的效果。在我们的实验中，结果表明，数值表面通量的选择有影响的收敛阶。惩罚型数值通量高耗散在所有的波，如LLF和HLL通量，出现的收敛顺序产生负面影响的奇数多项式次数N，相反的熵守恒的变体，即使多项式次数N产生负面影响。这种现象在低马赫数环境下更为明显。相比之下，对于接触波中具有较少耗散行为的数值表面通量，例如Roe通量，HLLC通量和熵守恒通量，增加了5波矩阵耗散，观察到N + 1的最佳收敛速度与马赫数无关。
Is the experimental order of convergence lower when using the entropy stable DGSEM-LGL variant? Recently, a debate on the question of the convergence behavior of the entropy stable nodal collocation discontinuous Galerkin spectral element method (DGSEM) with Legendre-Gauss-Lobatto nodes has emerged. Whereas it is well documented that the entropy conservative variant with no additional interface dissipation shows an odd-even behavior when testing its experimental convergence order, the results in the literature are less clear regarding the entropy stable version of the DGSEM-LGL, where explicit Riemann solver type dissipation is added at the element interfaces. We contribute to the ongoing discussion and present numerical experiments for the compressible Euler equations, where we investigate the effect of the choice of the numerical surface flux function. In our experiments, it turns out that the choice of the numerical surface flux has an impact on the convergence order. Penalty type numerical fluxes with high dissipation in all waves, such as the LLF and the HLL flux, appear to affect the convergence order negatively for odd polynomial degrees N, in contrast to the entropy conserving variant, where even polynomial degrees N are negatively affected. This behavior is more pronounced in low Mach number settings. In contrast, for numerical surface fluxes with less dissipative behavior in the contact wave such as e.g. Roe’s flux, the HLLC flux and the entropy conservative flux augmented with 5-wave matrix dissipation, optimal convergence rate of N + 1 independent of the Mach number is observed.
影响因子：
4.1
作者：
Chan, Jesse
通讯作者：
Chan, Jesse