The construction of discontinuous Galerkin (DG) methods for the compressible Euler or Navier-Stokes equations (NSE) includes the approximation of non-linear flux terms in the volume integrals. The terms can lead to aliasing and stability issues in turbulence simulations with moderate Mach numbers ($\text{Ma}\lesssim 0.3$), e.g. due to under-resolution of vortical dominated structures typical in large eddy simulations (LES). The kinetic energy or entropy is elevated in smooth, but under-resolved parts of the solution which are affected by aliasing. It is known that the kinetic energy is not a conserved quantity for compressible flows, but for small Mach numbers minor deviations from a conserved evolution can be expected. While it is formally possible to construct kinetic energy preserving (KEP) and entropy conserving (EC) DG methods for the Euler equations, due to the viscous terms in case of the NSE, we aim to construct kinetic energy dissipative (KED) or entropy stable (ES) DG methods on moving curved hexahedral meshes. The Arbitrary Lagrangian-Eulerian (ALE) approach is used to include the effect of mesh motion in the split form DG methods. First, we use the three dimensional Taylor-Green vortex to investigate and analyze our theoretical findings and the behavior of the novel split form ALE DG schemes for a turbulent vortical dominated flow. Second, we apply the framework to a complex aerodynamics application. An implicit LES split form ALE DG approach is used to simulate the transitional flow around a plunging SD7003 airfoil at Reynolds number $\text{Re}=40,000$ and Mach number $\text{Ma}=0.1$. We compare the standard nodal ALE DG scheme, the ALE DG variant with consistent overintegration of the non-linear terms and the novel KED and ES split form ALE DG methods in terms of robustness, accuracy and computational efficiency.

可压缩的Euler或Navier-Stokes方程（NSE）的不连续Galerkin（DG）方法的构造包括体积积分中非线性通量项的近似。这些术语会在马赫数中等的湍流模拟中导致混叠和稳定性问题（$\text{嘛}\lesssim 0.3$），例如由于大涡流模拟（LES）中典型的旋涡支配结构分辨率较低。动能或熵在受混叠影响的光滑但溶解度较低的部分中升高。众所周知，动能不是可压缩流的守恒量，但是对于马赫数较小的情况，可以预料到与守恒演化的微小偏差。尽管为Euler方程构造动能守恒（KEP）和熵守恒（EC）DG方法是正式可行的，但由于NSE的粘性项，我们的目标是构造动能耗散（KED）或熵稳定（ES）用于移动曲面六面体网格的DG方法。任意拉格朗日-欧拉（ALE）方法用于将网格运动的影响包括在拆分形式DG方法中。第一，我们使用三维泰勒-格林涡旋来研究和分析我们的理论发现以及湍流涡旋主导流的新型分裂形式ALE DG方案的行为。其次，我们将框架应用于复杂的空气动力学应用。隐式LES拆分形式ALE DG方法用于模拟雷诺数下暴跌的SD7003机翼周围的过渡流$\text{回覆}=40，000$ 和马赫数 $\text{嘛}=0.1$。在健壮性，准确性和计算效率方面，我们比较了标准节点ALE DG方案，具有一致的非线性项超积分的ALE DG变体以及新颖的KED和ES拆分形式ALE DG方法。