We present results of three-dimensional direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent gravity currents with a discontinuous Galerkin finite elements method. In particular, we consider the lock-exchange test case as a benchmark for gravity currents. Since, to the best of our knowledge, non-Boussinesq three-dimensional reference DNS are not available in the literature for this test case, we first perform a DNS experiment. The DNS provides an accurate description of the turbulent phenomena and highlights some differences with respect to the Boussinesq regime, like the non-symmetric pattern in the evolution of instabilities at the interfacial region and the fact that less turbulent structures are present due to greater stratification. A periodic pattern is also evident in the time evolution of turbulent mixing. The DNS is then employed to assess the performance of different LES models. In particular, we have considered the isotropic dynamic model and an anisotropic dynamic model. The LES results provide a first indication about the superiority of dynamic models with respect to no-model LES. However, the considered Reynolds numbers in the non-Boussinesq context are still too low to draw firm conclusions about the superiority of the present explicit LES approach with respect to an implicit LES approach.

中文翻译：

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非Boussinesq重力流的大涡模拟DG方法

我们使用不连续的伽辽金有限元方法展示了湍流重力流的三维直接数值模拟 (DNS) 和大涡模拟 (LES) 的结果。特别是，我们将锁定交换测试用例视为重力流的基准。由于据我们所知，此测试案例的文献中没有非 Boussinesq 三维参考 DNS，因此我们首先执行 DNS 实验。DNS 提供了湍流现象的准确描述，并突出了与 Boussinesq 机制的一些差异，例如界面区域不稳定性演变的非对称模式以及由于分层较大而存在较少湍流结构的事实。在湍流混合的时间演变中，周期性模式也很明显。然后使用 DNS 来评估不同 LES 模型的性能。特别地，我们已经考虑了各向同性动力学模型和各向异性动力学模型。LES 结果首次表明动态模型相对于无模型 LES 的优越性。然而，在非 Boussinesq 上下文中考虑的雷诺数仍然太低，无法得出关于当前显式 LES 方法相对于隐式 LES 方法的优越性的确切结论。