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The astonishing diversity in the observed planetary population requirestheoretical efforts and advances in planet formation theories. Numericalapproaches provide a method to tackle the weaknesses of current planetformation models and are an important tool to close gaps in poorly constrainedareas. We present a global disk setup to model the first stages of giant planetformation via gravitational instabilities (GI) in 3D with the block-structuredadaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, weexplore the impact of AMR techniques on the fragmentation and clumping due tolarge-scale instabilities using different AMR configurations. Additionally, weseek to derive general resolution criteria for global simulations ofself-gravitating disks of variable extent. We run a grid of simulations withvarying AMR settings, including runs with a static grid for comparison, andstudy the effects of varying the disk radius. Adopting a marginally stable diskprofile (Q_init=1), we validate the numerical robustness of our model fordifferent spatial extensions, from compact to larger, extended disks (R_disk =10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combiningour findings from the resolution and parameter studies we find a lower limit ofthe resolution to be able to resolve GI induced fragmentation features anddistinct, turbulence inducing clumps. Irrespective of the physical extension ofthe disk, topologically disconnected clump features are only resolved if thefragmentation-active zone of the disk is resolved with at least 100 cells,which holds as a minimum requirement for all global disk setups. Oursimulations illustrate the capabilities of AMR-based modeling techniques forplanet formation simulations and underline the importance of balancedrefinement settings to reproduce fragmenting structures.

Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques