Warped disk evolution in grid-based simulations

Context. Multiple observations have offered evidence that a significant fraction of protoplanetary disks contain warps. A warp in a disk evolves over time, affecting the appearance and shape of shadows and arcs. It also greatly influences kinematic signatures. Understanding warp evolution helps provide valuable insights into its origins. Aims. Thus far, numerous theoretical studies of warped disks have been conducted using methods based on smoothed particle hydrodynamics (SPH). In our approach, we use a grid-based method in spherical coordinates, which offers notable advantages. For instance, it allows for an accurate modeling of low viscosity values. Furthermore, the resolution does not depend on density or mass of the disk and permits surface structures to be resolved. Methods. We performed 3D simulations using FARGO3D to simulate the evolution of a warped disk and compared the results to 1D models. We extensively investigated the applicability of grid-based methods to misaligned disks and tested their dependence on the grid resolution as well as the disk viscosity. Results. We find that grid-based hydrodynamic simulations are capable of simulating disks not aligned to the grid geometry. Our 3D simulation of a warped disk offers an apt comparison with 1D models in terms of the evolution of inclination. However, we also found a twist that is not captured in 1D models. After thorough analysis, we suspect this to be a physical effect possibly caused by non-linear effects neglected in the 1D equations. Evaluating the internal dynamics, we found sloshing and breathing motions, as predicted in local shearing box analysis. They may become supersonic, possibly leading to strong consequences for kinematic observations. Conclusions. Warped disks can be accurately modeled in 3D grid-based hydrodynamics simulations when using a reasonably good resolution, especially in the θ-direction. We find a good agreement with the linear approximation of the sloshing motion, which highlights the reliability of 1D models.