论文标题
分裂形式不连续的Galerkin方法，并应用于解决不足的湍流低模数流量
Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows
论文作者
论文摘要
用于可压缩欧拉或Navier-Stokes方程（NSE）的不连续Galerkin（DG）方法的构建包括体积积分中非线性通量项的近似值。这些术语可能导致具有中等马赫数（MA <0.3）的湍流模拟中的混溶性和稳定性问题，例如由于大型涡流模拟（LES）中典型的涡流支配结构的分辨率不足。动能或熵在平滑的溶液中升高，但溶液的分辨部分不受混蛋影响。众所周知，动能不是可压缩流的保守量，但是对于小马赫数来说，可以预期与保守进化的小偏差。由于NSE的粘性术语，虽然可以正式构建欧拉方程（EC）保存（EC）DG方法的熵（EC）DG方法，但我们旨在构建动态弯曲的六角形六角形六角甲甲中的DG方法。任意的Lagrangian-Eulerian（ALE）方法用于将网格运动的效果包括在分裂形式DG方法中。首先，我们使用三维的泰勒绿色涡流来研究和分析我们的理论发现和新颖的拆分形成啤酒DG方案的行为，以进行湍流的涡流主导的流动。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Reynolds Number in = 40，000和Mach Number MA = 0.1的跌落SD7003机翼周围的过渡流。我们比较了标准节点ALE DG方案，即非线性术语一致的ALE DG变体，而新颖的KED和ES拆分形式ALE DG方法就稳健性，准确性和计算效率而言。
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 (Ma < 0.3), e.g. due to under-resolution of vortical dominated structures typical in large eddy simulations (LES). The kinetic energy or entropy are 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 Re = 40, 000 and Mach number 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.
