  We consider the problem of numerically computing the quantum dynamics of an
electron in twisted bilayer graphene. The challenge is that atomic-scale models
of the dynamics are aperiodic for generic twist angles because of the
incommensurability of the layers. The Bistritzer-MacDonald PDE model, which is
periodic with respect to the bilayer's moir\'e pattern, has recently been shown
to rigorously describe these dynamics in a parameter regime. In this work, we
first prove that the dynamics of the tight-binding model of incommensurate
twisted bilayer graphene can be approximated by computations on finite domains.
The main ingredient of this proof is a speed of propagation estimate proved
using Combes-Thomas estimates. We then provide extensive numerical computations
which clarify the range of validity of the Bistritzer-MacDonald model.
