2-D preplanetary accretion disks - I. Hydrodynamics, chemistry, and mixing processes

Aims. We outline a numerical method to calculate spatially two-dimensional (2-D) reactive flows and mixing processes in preplanetary accretion disks and present first results. The numerical efficiency and robustness is demonstrated by following the hydrodynamical and chemical evolution of the disk from a highly non-stationary dynamical switch-on phase asymptotically into the quasi-stationary, viscous accretion regime. One major question we address is the C-, H-, O-chemistry. The leit-motif of our investigation is the attempt to preserve as much consistency as possible when modelling the hydrodynamical, chemical, transport/mixing processes and their mutual interactions in preplanetary disks. Methods. We use an explicit scheme for solving the Navier-Stokes equations combined with an implicit solver for the energy equation. The viscosity coefficient is modelled according to the so-called beta-prescription of turbulent viscosity. In contrast to the well-known alpha-viscosity, the beta-parameterization of the viscosity warrants physical consistency if self-gravitation of the disk material is to be taken into account. However, up to now we have neglected self-gravitation. For the radiative energy transport we have adopted the (grey) Eddington approximation. The opacity is assumed to be caused by microscopic dust particles. Diffusive mixing of the various chemical species is modelled by taking the diffusion coefficient, D, proportional to the (turbulent) viscosity, nu(turb). For comparison purposes, we have considered two extreme choices of the Schmidt number, S := nu(turb)/D, that is, S = 1 (D = nu(turb)) and S = infinity (D = 0, i.e., no diffusive mixing at all), respectively. We have not yet included coagulation processes and grain growth. Results. The main outcome of the 2-D simulations so far carried out is a characteristic circulation pattern of the quasi-stationary accretion flow: Near the disk's equatorial plane which is assumed to be a plane of symmetry the material moves in the outward direction, whereas the accretion flow proper develops in higher altitudes of the disk. Species that are produced or undergo chemical reactions in the warm inner zones of the disk are advectively transported into the cool outer regions. At the same time, they either diffusively mix up with the surrounding material or freeze out on the dust grains to form ice-coated particles. By virtue of the large-scale circulation, which is driven by viscous angular momentum transfer, advective transport dominates diffusive mixing in the outer part of the disk.