Princeton University Thunch Talk

Rotationally supported, cold, gaseous disks are ubiquitous in astrophysics and appear in a diverse set of systems, such as protoplanetary disks, accretion disks around black holes, or large spiral galaxies. By using a cold, two-dimensional, gaseous, keplerian disk I show in this talk that traditional Lagrangian methods such as SPH as well as codes using a static cartesian grid fail to evolve the disk accurately for several orbits. The moving-mesh method as implemented in the AREPO code performs better but the so-called mesh noise on the grid scale finally destabilizes the disk. To increase the local resolution I present a novel implementation of the shearing-box approximation in AREPO. The implementation offers manifest translational invariance across the shearing-box boundaries and offers continuous local adaptivity. But again the unstructured mesh leads to grid noise. I show that this can be rectified by high-order integrations of the flux over mesh boundaries. The higher-order integration also removes the noise in global simulations which leads the disk from the beginning of my talk to be stable. As first applications of the new shearing-box implementation, I present parameter studies for the magnetorotational instability and gravitational instability.