Abstract Stars are born with a surrounding disk made up of gas entrained by dusty and icy particles, which are the building material for planetary systems. The evolution from small grains towards planetesimals and embryos is regulated by turbulence-driven transport and collisions. Likewise, the migration and growth of planets depends on the gas turbulence. In order to make interpretations of disk observations, one needs to model the turbulent state and the dynamic evolution in these disks. Typical observations of molecular lines provide us with information about the velocity deviation from laminar rotation, and continuum observations of emitted and scattered light helps us determine the spatial and size distribution of dust. The purpose of this review is to provide a guide book on how to set up hydrodynamic and radiation hydrodynamic simulations of a disk around a young star reflecting the current state of code development. These models can then be used to study the effect of turbulence on the distribution and evolution of dust up to planetesimals and planetary embryos, as well as to study the interaction of planets with the disk gas. We will focus on the effects of radiation transport on dynamic stability in global three-dimensional simulations and, therefore, neglect the effects of self-gravity, particle feedback and magnetic fields to some later iteration of the topic.
Klahr et al. (Wed,) studied this question.