  The dynamics of accreting and outgoing flows around compact objects depends
crucially on the strengths and configurations of the magnetic fields therein,
especially of the large-scale fields that remain coherent beyond turbulence
scales. Possible origins of these large-scale magnetic fields include flux
advection and disc dynamo actions. However, most numerical simulations have to
adopt an initially strong large-scale field rather than allow them to be
self-consistently advected or amplified, due to limited computational
resources. The situation can be partially cured by using sub-grid models where
dynamo actions only reachable at high resolutions are mimicked by artificial
terms in low-resolution simulations. In this work, we couple thin-disc models
with local shearing-box simulation results to facilitate more realistic
sub-grid dynamo implementations. For helical dynamos, detailed spatial profiles
of dynamo drivers inferred from local simulations are used, and the nonlinear
quenching and saturation is constrained by magnetic helicity evolution. In the
inner disc region, saturated fields have dipole configurations and the plasma
$\beta$ reaches $\simeq 0.1$ to $100$, with correlation lengths $\simeq h$ in
the vertical direction and $\simeq 10h$ in the radial direction, where $h$ is
the disc scale height. The dynamo cycle period is $\simeq 40$ orbital time
scale, compatible with previous global simulations. Additionally, we explore
two dynamo mechanisms which do not require a net kinetic helicity and have only
been studied in shearing-box setups. We show that such dynamos are possible in
thin accretion discs, but produce field configurations that are incompatible
with previous results. We discuss implications for future general-relativistic
magnetohydrodynamics simulations.
