We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit time stepping is used for the temporal discretization, which allows for a much larger time step size for stability compared to explicit methods, especially for low-Mach number flows and/or on highly distorted meshes. Ample numerical results are presented to showcase the good performance of our proposed scheme.

翻译：我们采用离散能量变分方法，提出了用于可压缩流体的高阶变分拉格朗日有限元格式。所提出的空间离散格式具有质量/动量/能量守恒及熵稳定性特性。时间离散采用全隐式步进策略，相较于显式方法，该策略可显著增大稳定性所需的步长，尤其适用于低马赫数流动和/或高度畸变网格情形。文中通过丰富的数值实验结果充分验证了所提方法的优良性能。