Split form ALE discontinuous Galerkin methods with applications to under-resolved turbulent low-Mach number flows

[摘要] 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 less than or similar to 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 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. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-11-15

[关键词] Implicit large eddy simulation;Discontinuous Galerkin;Arbitrary Lagrangian-Eulerian approach;De-aliasing;Kinetic energy dissipative methods;Entropy stable methods