1+1D implicit disk computations

TL;DR

This paper introduces an implicit numerical method for simulating the evolution of gaseous disks in axial symmetry, incorporating self-gravity and adaptive grids, and demonstrates its effectiveness through various tests.

Contribution

It presents a novel implicit scheme for radiation hydrodynamics in 1+1D disks, including self-gravity and adaptive grid techniques, with validation against analytical and long-term evolution models.

Findings

The method accurately reproduces analytical solutions.

It effectively models viscous evolution and disk depletion.

Inner boundary conditions significantly influence disk structure.

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.