We demostrate the importance of general relativistic apsidal
precession in warped black hole accretion discs by comparing
three-dimensional smoothed particle hydrodynamic simulations in which
this effect is first neglected, and then included. If apsidal
precession is neglected, we confirm the results of an earlier
magnetohydrodynamic simulation by Krolik & Hawley (2015). We thus show
that at least in this case the alpha-viscosity model produces very
similar results to those of simulations where angular momentum
transport is due to the MRI. This is shown below, with the twist (left)
and tilt (right) shown in the same style as Krolik & Hawley (2015).
We then include apsidal precession in our simulations, as in Nealon,
Price & Nixon (2015). The comparison of twist is shown here, with
apsidal precession neglected on the left and included on the right.
A comparison of the tilt with and without apsidal precession
similarly identifies that including apsidal precession significantly
changes the predicted disc evolution. The final profile with a nonzero
inner edge tilt and an inner edge oscillation is consistent with
published analytic results.
Our simulation inclined at 12 degrees shows no evidence of disc
breaking, as in Krolik & Hawley (2015). We repeat our simulation at 30
degrees for the same amount of time, and plot the density of both
below. As the discs evolve, the inner ring of the highly inclined disc
(right) has a small inclination when compared to the outer ring.