  The shock induced mixing of two gases separated by a perturbed interface is
investigated through Large Eddy Simulation (LES) and Direct Numerical
Simulation (DNS). In a simulation, physical dissipation of the velocity field
and species mass fraction often compete with numerical dissipation arising from
the errors of the numerical method. In a DNS the computational mesh resolves
all physical gradients of the flow and the relative effect of numerical
dissipation is small. In LES, unresolved scales are present and numerical
dissipation can have a large impact on the flow, depending on the computational
mesh. A suite of simulations explores the space between these two extremes by
studying the effects of grid resolution, Reynolds number and numerical method
on the mixing process. Results from a DNS are shown using two different codes,
which use a high- and low-order numerical method and show convergence in the
temporal and spectral dependent quantities associated with mixing. Data from a
coarse LES are also presented and include a grid convergence study. A model for
an effective viscosity is proposed which allows for an a posteriori analysis of
the simulation data that is agnostic to the LES model, numerics and the
physical Reynolds number of the simulation. An analogous approximation for an
effective species diffusivity is also presented. This framework can then be
used to estimate the effective Reynolds number and Schmidt number of future
simulations, elucidate the impact of numerical dissipation on the mixing
process for an arbitrary numerical method and provide guidance for resolution
requirements of future calculations
