  Large eddy simulation (LES) has been increasingly used to tackle
vortex-dominated turbulent flows. In LES, the quality of the simulation results
hinges upon the quality of the numerical discretizations in both space and
time. It is in this context we perform a Fourier analysis of several popular
methods in LES including the discontinuous Galerkin (DG), finite difference
(FD), and compact difference (CD) methods. We begin by reviewing the
semi-discrete versions of all methods under-consideration, followed by a
fully-discrete analysis with explicit Runge-Kutta (RK) time integration
schemes. In this regard, we are able to unravel the true dispersion/dissipation
behavior of DG and Runge-Kutta DG (RKDG) schemes for the entire wavenumber
range. The physical-mode is verified to be a good approximation for the
asymptotic behavior of these DG schemes in the low wavenumber range. After
that, we proceed to compare the DG, FD, and CD methods in dispersion and
dissipation properties. Numerical tests are conducted using the linear
advection equation to verify the analysis. In comparing different methods, it
is found that the overall numerical dissipation strongly depends on the time
step. Compact difference (CD) and central finite difference (FD) schemes, in
some particular settings, can have more numerical dissipation than the DG
scheme with an upwind flux. This claim is then verified through a numerical
test using the Burgers' equation.
