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.