  Observations show evidence that a significant fraction of protoplanetary
disks contain warps. A warp in a disk evolves in time affecting the appearance
of shadows and greatly influencing kinematic signatures. So far, many
theoretical studies of warped disks have been conducted using Smoothed Particle
Hydrodynamics (SPH) methods. In our approach, we use a grid-based method in
spherical coordinates which has notable advantages: the method allows for
accurate modelling of low viscosity values and the resolution does not depend
on density or mass of the disk, which allows surface structures to be resolved.
We perform 3D simulations using FARGO3D to simulate the evolution of a warped
disk and compare the results to one-dimensional models using a ring code.
Additionally, we extensively investigate the applicability of grid-based
methods to misaligned disks and test their dependency on grid resolution as
well as disk viscosity. We find that grid-based simulations are capable of
simulating disks not aligned to the grid geometry. Our three-dimensional
simulation of a warped disk compares well to one-dimensional models in
evolution of inclination. However, we find a twist which 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 one-dimensional
equations. Evaluating the internal dynamics, we find sloshing and breathing
motions as predicted in local shearing box analysis. They can become
supersonic, which may have consequences on kinematic observations of warped
disks. Warped disks can be accurately modelled in 3D grid-based simulations
when using reasonably good resolution, especially in the $\theta$-direction. We
find good agreement with the linear approximation of the sloshing motion which
highlights the reliability of 1D models.
