  We present results of three-dimensional Direct Numerical Simulations (DNS)
and Large Eddy Simulations (LES) of turbulent gravity currents with a
Discontinuous Galerkin (DG) Finite Elements method. In particular, we consider
the three-dimensional lock-exchange test case as a typical 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 three-dimensional DNS allows
to correctly capture the loss of coherence of the three-dimensional turbulent
structures, providing an accurate description of the turbulent phenomena taking
place in gravity currents. The DNS is then employed to assess the performance
of different LES models. In particular, we have considered the Smagorinsky
model, the isotropic dynamic model and an anisotropic dynamic model. The LES
results highlight the excessively dissipative nature of the Smagorinsky model
with respect to the dynamic models and the fact that the anisotropic dynamic
model performs slightly better with respect to its isotropic counterpart.
