In large eddy simulations (LES) the transfer of energy and tracer
variance across scales is explicitly resolved down to the grid scale,
where these quantities are dissipated. The dissipation can be
explicit, with a closure at the sub-grid scale, or implicit, by
embedding the dissipation into the discretized transport terms,
resulting in what is known as implicit LES (ILES). The two main
numerical ingredients of ILES are upwinding and nonlinear
interpolations for the transport terms. However, it gives an essential
role to the numerical methods employed, which may frighten the
physicist. Moreover, as the dissipation is hidden in the transport,
there is no parameter controlling it, such as the Reynolds number, and
it is difficult to diagnose its intensity. In this talk, I will show
how the discrete differential geometry offers a unifying framework to
discretize the transport terms of fluid equations. The main idea is to
consider the model variables (momentum, buoyancy, pressure, etc.) as
differential forms, and discretize the transport terms as Lie
derivatives. The upwinding and the nonlinear interpolations are
naturally performed on the interior product. The second point is to
show how, by extracting the irreversible part of the discretized
transport, one can compute the local dissipation rate of energy,
tracer variance, enstrophy etc.