  We present the results of smoothed particle hydrodynamics (SPH) simulations
of the disc around the young, eccentric stellar binary HD 104237. We find that
the binary clears out a large cavity in the disc, driving a significant
eccentricity at the cavity edge. This then precesses around the binary at a
rate of $\dot{\varpi} = 0.48^{\circ}T_{\mathrm{b}}^{-1}$, which for HD 104237
corresponds to 40 years. We find that the accretion pattern into the cavity and
onto the binary changes with this precession, resulting in a periodic accretion
variability driven purely by the physical parameters of the binary and its
orbit. For each star we find that this results in order of magnitude changes in
the accretion rate. We also find that the accretion variability allows the
primary to accrete gas at a higher rate than the secondary for approximately
half of each precession period. Using a large number of 3-body integrations of
test particles orbiting different binaries, we find good agreement between the
precession rate of a test particle and our SPH disc precession. These rates
also agree very well with the precession rates predicted by the analytic theory
of Leung & Lee (2013), showing that their prescription can be accurately used
to predict long-term accretion variability timescales for eccentric binaries
accreting from a disc. We discuss the implications of our result, and suggest
that this process provides a viable way of preserving unequal mass ratios in
accreting eccentric binaries in both the stellar and supermassive black hole
regimes
