论文标题
在不连续的Galerkin方案中解决不足的湍流的跳罚稳定技术
Jump penalty stabilisation techniques for under-resolved turbulence in discontinuous Galerkin schemes
论文作者
论文摘要
最近已经提出了针对连续和不连续的高级盖尔金方案[1,2,3]提出的跳跃惩罚稳定技术。稳定依赖于元素界面处的梯度或溶液不连续性，以在数值方案中纳入局部数值扩散。这种扩散是一个隐式亚网格模型，并稳定了稳定的湍流模拟。 本文研究了跳跃惩罚稳定方法（惩罚梯度或解决方案）对湍流制度中高阶不连续的Galerkin方案的稳定和改善的影响。我们使用特征分析，1D非线性汉堡方程（模仿湍流级联反应）和3D湍流Navier-Stokes模拟（Taylor-Green Vortex问题）分析了这些方案。 我们表明，由于分散分散特征的改善（与非占层化的方案相比，两种跳罚稳定技术可以稳定稳定的模拟，并为湍流提供了准确的结果。数值结果表明，与原始的未获得的方案和经典的显式亚网格模型（Smagorisnky和Vreman）相比，提出的跳跃惩罚稳定了稳定的较低的模拟并改善了模拟。
Jump penalty stabilisation techniques have been recently proposed for continuous and discontinuous high order Galerkin schemes [1,2,3]. The stabilisation relies on the gradient or solution discontinuity at element interfaces to incorporate localised numerical diffusion in the numerical scheme. This diffusion acts as an implicit subgrid model and stablises under-resolved turbulent simulations. This paper investigates the effect of jump penalty stabilisation methods (penalising gradient or solution) for stabilisation and improvement of high-order discontinuous Galerkin schemes in turbulent regime. We analyse these schemes using an eigensolution analysis, a 1D non-linear Burgers equation (mimicking a turbulent cascade) and 3D turbulent Navier-Stokes simulations (Taylor-Green Vortex problem). We show that the two jump penalty stabilisation techniques can stabilise under-resolved simulations thanks to the improved dispersion-dissipation characteristics (when compared to non-penalised schemes) and provide accurate results for turbulent flows. The numerical results indicate that the proposed jump penalty stabilise under-resolved simulations and improve the simulations, when compared to the original unpenalised scheme and to classic explicit subgrid models (Smagorisnky and Vreman).
