This numerical work investigates the potential of a high-order finite-difference spectral vanishing viscosity approach to simulate gravity currents at high Reynolds numbers. The method introduces targeted numerical dissipation at small scales through altering the discretisation of the second derivatives of the viscous terms in the incompressible Navier-Stokes equations to mimic the spectral vanishing viscosity (SVV) operator, originally designed for the regularisation of spectral element method (SEM) solutions of pure advection problems. Using a sixth-order accurate finite-difference scheme, the adoption of the SVV method is straightforward and comes with a negligible additional computational cost. In order to assess the ability of this high-order finite-difference spectral vanishing viscosity approach, we performed large-eddy simulations (LES) of a gravity current in a channelised lock-exchange set-up with our SVV model and with the well-known explicit static and dynamic Smagorinsky sub-grid scale (SGS) models. The obtained data are compared with a direct numerical simulation (DNS) based on more than 800 million mesh nodes, and with experimental measurements. A framework for the energy budget is introduced to investigate the behaviour of the gravity current. First, it is found that the DNS is in good agreement with the experimental data for the evolution of the front location and velocity field as well as for the stirring and mixing inside the gravity current. Secondly, the LES performed with less than 0.4% of the total number of mesh nodes compared to the DNS, can reproduce the main features of the gravity currents, with the SVV model yielding slightly more accurate results. It is also found that the dynamic Smagorinsky model performs better than its static version. For the present study, the static and dynamic Smagorinsky models are 1.8 and 2.5 times more expensive than the SVV model, because the latter does not require the calculation of explicit SGS terms in the Navier-Stokes equations nor spatial filtering operations.

这项数值研究研究了在高雷诺数下模拟高重力流的高阶有限差分光谱消失粘度方法的潜力。该方法通过更改不可压缩的Navier-Stokes方程中粘性项的二阶导数的离散化以模仿光谱消失粘度（SVV）算子，从而在小规模范围内引入了目标数值耗散，该算子最初是为光谱元素方法（SEM）的正则化而设计的）纯对流问题的解决方案。使用六阶精确有限差分方案，SVV方法的采用非常简单，并且额外的计算成本可忽略不计。为了评估这种高阶有限差分光谱消失粘度方法的能力，我们使用SVV模型以及著名的显式静态和动态Smagorinsky子网格比例（SGS）模型，在通道锁定交换设置中对重力电流进行了大涡模拟（LES）。将获得的数据与基于8亿多个网格节点的直接数值模拟（DNS）进行比较，并与实验测量结果进行比较。引入了能量预算框架来研究重力流的行为。首先，发现DNS与前端位置和速度场的演化以及重力流内部的搅拌和混合的实验数据非常吻合。其次，与DNS相比，LES的网格节点总数不到0.4％，可以重现引力流的主要特征，SVV模型产生的结果会稍微准确一些。还发现动态Smagorinsky模型的性能优于静态模型。对于本研究，静态和动态Smagorinsky模型的成本分别是SVV模型的1.8倍和2.5倍，因为SVV模型不需要计算Navier-Stokes方程中的显式SGS项，也不需要空间滤波操作。