  Recent developments in non-ideal magnetohydrodynamic simulations of
protoplanetary disks suggest that instead of being traditional turbulent
(viscous) accretion disks, they have a largely laminar flow with accretion
driven by large-scale wind torques. These disks are possibly threaded by
Hall-effect generated large-scale horizontal magnetic fields. We have examined
the dynamics of the corotation region of a low mass planet embedded in such a
disk and the evolution of the associated migration torque. These disks lack
strong turbulence and associated turbulent diffusion, and the presence of a
magnetic field and radial gas flow presents a situation outside the
applicability of previous corotation torque theory. We summarize the analytical
analysis of the corotation torque, give details on the numerical methods used,
and in particular the relative merits of different numerical schemes for the
inviscid problem.
