In this study we employ von Neumann analyses to investigate the disper-
sion, dissipation, group velocity, and error properties of several fully discrete
flux reconstruction (FR) schemes. We consider three FR schemes paired
with two explicit Runge-Kutta (ERK) schemes and two singly diagonally
implicit RK (SDIRK) schemes. Key insights include the dependence of
high-wavenumber numerical dissipation, relied upon for implicit large eddy
simulation (ILES), on the choice of temporal scheme and time-step size.
Also, the wavespeed characteristics of fully-discrete schemes and the relative
dominance of temporal and spatial errors as a function of wavenumber and
time-step size are investigated. Salient properties from the aforementioned
theoretical analysis are then demonstrated in practice using linear advection
test cases. Finally, a Burgers turbulence test case is used to demonstrate the
importance of the temporal discretisation when using FR schemes for ILES.