1+1D implicit disk computations

Abstract

We present an implicit numerical method to solve the time-dependent equations of radiation hydrodynamics (RHD) in axial symmetry assuming hydrostatic equilibrium perpendicular to the equatorial plane (1+1D) of a gaseous disk. The equations are formulated in conservative form on an adaptive grid and the corresponding fluxes are calculated by a spacial second order advection scheme. Self-gravity of the disk is included by solving the Possion equation. We test the resulting numerical method through comparison with a simplified analytical solution as well as through the long term viscous evolution of protoplanetary disk when due to viscosity matter is transported towards the central host star and the disk depletes. The importance of the inner boundary conditions on the structural behaviour of disks is demonstrated with several examples.

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• Time-dependent long-term hydrodynamic simulations of the inner protoplanetary disk III: The influence of photoevaporation
• The post-disk (or primordial) spin distribution of M dwarf stars
• Protoplanetary disks around magnetized young stars with large-scale magnetic fields I: Steady-state solutions
• On the diversification and dissipation of protoplanetary disks