Abstract The discontinuous Galerkin (DG) method is a promising numerical method to enable high- order simulations of turbulent flows associated with complex geometries. The method allows implicit large eddy simulations, however affordable simulations of very high Reynolds’ number flows require wall models. In addition, high Reynolds’ number typically implies the simulations are under-resolved. This becomes problematic as a high polynomial order may lead to aliasing instabilities on coarse grids, often leading to blow-up. Split formulations, first introduced in the finite-difference community, are a promising approach to address this problem. The present study shows that split forms and wall models can be used to enable the discontinuous Galerkin method to do very high Reynolds’ number simulations on unstructured grids.

中文翻译：

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关于使用分裂形式和壁建模在贴身非结构化网格上实现精确的高雷诺数不连续伽辽金模拟

摘要 不连续伽辽金 (DG) 方法是一种很有前途的数值方法，可以对与复杂几何形状相关的湍流进行高阶模拟。该方法允许隐式大涡模拟，但是非常高的雷诺数流动的负担得起的模拟需要壁模型。此外，高雷诺数通常意味着模拟未得到充分解决。这变得有问题，因为高多项式阶可能导致粗网格上的混叠不稳定性，通常会导致爆炸。分裂公式首先在有限差分社区中引入，是解决这个问题的一种很有前途的方法。本研究表明，分裂形式和壁模型可用于使不连续伽辽金方法能够在非结构化网格上进行非常高的雷诺数模拟。