AI 中文总结
该研究以开尔文-亥姆霍兹问题为基准，对比四种数值格式，探究可压缩欧拉方程耗散弱解的选择准则及选择泛函对数值扩散的敏感性。
AI 中文摘要
我们对可压缩欧拉方程耗散弱解的选择准则进行数值研究。以开尔文-亥姆霍兹问题为基准，我们比较四种标准数值格式：粘性有限体积（VFV）方法、离散速度玻尔兹曼有限体积（DVBFV）方法、龙格-库塔间断伽辽金（RKDG）方法和间断伽辽金谱元方法（DGSEM），并证明每种格式可能收敛到不同的耗散弱解。我们基于熵产生、总能量和能量缺陷对这些解评估若干选择准则，并研究选择泛函对各格式固有数值扩散的敏感性。
英文摘要
We numerically investigate selection criteria for dissipative weak solutions of the compressible Euler equations. Using the Kelvin-Helmholtz problem as a benchmark, we compare four standard numerical schemes - the viscous finite volume (VFV) method, the discrete velocity Boltzmann finite volume (DVBFV) method, the Runge-Kutta discontinuous Galerkin (RKDG) method, and the discontinuous Galerkin spectral element method (DGSEM), and demonstrate that each may converge to a different dissipative weak solution. We evaluate these solutions with respect to several selection criteria based on entropy production, total energy, and energy defect, and examine the sensitivity of selection functionals to the numerical diffusion inherent in each scheme.
