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RANS simulations for the turbulent uniform and channel flow using HDG for incompressible flow

机译：使用HDG对不可压缩流的湍流均匀和通道流的Rans模拟

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1 Introduction All the industrial flow solvers dedicated to high Reynolds turbulent flows for industrial configurations are based on a formally second order accurate temporal and spatial discretization. There is a strong need for more accurate discretization approaches in many fields like computational acoustics or Large Eddy simulation which are still out of reach of systematic industrial studies. During the last ten years, several numerical methodologies have emerged, mainly for compressible flows, which look promising in terms of accuracy, computational cost and numerical robustness. A few of them concerned with incompressible flows which need very specific developments that will be the topic of this extended abstract. Numerous attempts were made to achieve high-order accurate unsteady INS solvers. However, plenty of them fails to satisfy conservation laws. Mass, momentum, and energy conservation are essential for the robustness of the method when solving the unsteady INS. Laminar flow and flows that typically have Reynolds numbers below 10~4 are not affected greatly by the lack of conservation. However, for high Reynolds numbers, i.e. turbulent flows, conservation laws must be satisfied in the numerical method to have a stable one. In order to satisfy the conservation laws numerically, the approximate velocity must be exactly divergence-free to have an energy-stable and momentum conserving method. A proposed method was developed that uses the same idea of approximation spaces mentioned in Rhebergen and Wells (2018), but with different penalization. In addition, the approximation spaces were modified so that the method can be applied for quadrilateral and hexahedral meshes.
机译：1简介所有专用于高雷诺兹的工业流量紊乱的工业配置的所有工业流量求解器都基于正式的二阶准确的时间和空间离散化。在许多领域中具有更加准确的离散化方法，如计算声学或大型涡流模拟，其仍然超出系统的工业研究。在过去的十年中，出现了几种数值方法，主要用于可压缩流，这在准确性，计算成本和数值鲁棒方面看起来很有希望。其中一些关注不可压缩的流动，需要具有非常具体的发展，这将是这一扩展摘要的主题。进行了许多尝试，以实现高阶准确的不稳定INS求解器。但是，他们中的许多都没有满足保护法。质量，动量和节能对于解决不稳定的INS时，对方法的稳健性至关重要。在缺乏保护的情况下，通常具有低于10〜4的雷诺数的流体流量和流量不会受到大量影响。然而，对于高雷诺数，即湍流流动，在数值方法中必须满足保护法，以具有稳定的方法。为了在数值上满足保护法，必须完全偏离近似速度，以具有能量稳定和动量节省的方法。开发了一种提出的方​​法，该方法使用了rhebergen和井（2018）中提到的相同近似空间的想法，但在不同的惩罚中。另外，修改了近似空间，使得该方法可以应用于四边形和六边形网格。

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