  We aim to develop a simple prescription for migration and accretion in 1D
disc models, calibrated with results of 3D hydrodynamic simulations. Our focus
lies on non-self-gravitating discs, but we also discuss to what degree our
prescription could be applied when the discs are self-gravitating.
  We study migration using torque densities. Our model for the torque density
is based on existing fitting formulas, which we subsequently modify to prevent
premature gap-opening. At higher planetary masses, we also apply torque
densities from hydrodynamic simulations directly to our 1D model. These torque
densities allow modelling the orbital evolution of an initially low-mass planet
that undergoes runaway-accretion to become a massive planet. The two-way
exchange of angular momentum between disc and planet is included. This leads to
a self-consistent treatment of gap formation that only relies on directly
accessible disc parameters. We present a formula for Bondi- and Hill- gas
accretion in the disc-limited regime. This formula is self-consistent in the
sense that mass is removed from the disc in the location from where it is
accreted.
  We find that the resulting evolution in mass and semi-major axis in the 1D
framework is in good agreement with those from 3D hydrodynamical simulations
for a range of parameters.
  Our prescription is valuable for simultaneously modelling migration and
accretion in 1D-models. We conclude that it is appropriate and beneficial to
apply torque densities from hydrodynamic simulations in 1D models, at least in
the parameter space we study here. More work is needed to in order to determine
whether our approach is also applicable in an even wider parameter space and in
situations with more complex disc thermodynamics, or when the disc is
self-gravitating.
